User:Z E U S/1

$$38756928539284314123049008318026368438221998823818157701981611847981052946086230517779418600353541323118851294249609652880788683611489679696027792584816798286546439597625664031512417580575356281435570813989103921311479584760379287707724243274506906164504370947981399049559728910046659604440048209472^{104536113776305096559688240973949256190167194032892185858412761355595972804612264795071065166934350812256523818708562538374700528878580738296832597039986338236668384742302941726521217771506223372597117591535962383854860697754550083442105428640948558383002934553977298669928578507173938623814610729897}\,$$

$$\left ( \frac{38756928539284314123049008318026368438221998823818157701981611847981052946086230517779418600353541323118851294249609652880788683611489679696027792584816798286546439597625664031512417580575356281435570813989103921311479584760379287707724243274506906164504370947981399049559728910046659604440048209472^{104536113776305096559688240973949256190167194032892185858412761355595972804612264795071065166934350812256523818708562538374700528878580738296832597039986338236668384742302941726521217771506223372597117591535962383854860697754550083442105428640948558383002934553977298669928578507173938623814610729897}}{105966046330769304886073092822589624299830328759415167682442574582167794055871049254769493025329667962976212114266006479387868344184327682711205269031458046574665080524048024146643248425659407860467229982524540867201511530051391067636012941954138057614734658851306048235208397343325303969187863015429} \right )$$

$$\left ( \sqrt[\left ( y^{(x)}(x) \right )]\cfrac{y^{(G^G -G)}(x) - y^{(e^x -Gy^{(G)}(x))}(x)}{\left (\cfrac{y(x) - y'(x)}{e^{[y(x) +y(x)]}} \right )y^{(Gx)}(x-1) +1} \right )- \left   (\sum_{k=1}^\infty y^{(x)}(x-k)\right )^{(y'(x)-y(x))^{(y(x) + e^{y'(x)})}} +1 = 0$$

$$\ y^{(x)}(x) = e^x$$

$$\ y(x) = e^x$$

$$	\iiiint_{\iiiint_{\iiiint_{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt}^{\iiiint_{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt}^{\iiiint_{F}^{U} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt} \, dx\,dy\,dz\,dt$$

$$\begin{align} &ax+b =0, \\ &r_1 = \frac{-b}{a}\\ &ax^2+bx+c=0, \\ &r_1 = \frac{-b + \sqrt {b^2-4ac}}{2a}, \\ &r_2 = \frac{-b - \sqrt {b^2-4ac}}{2a}, \\ &ax^3+bx^2+cx+d=0,\\

&r_1 = -\frac{b}{3 a}-\frac{1}{3 a} \sqrt[3]{\tfrac12\left[2 b^3-9 a b c+27 a^2 d+\sqrt{\left(2 b^3-9 a b c+27 a^2 d\right)^2-4 \left(b^2-3 a c\right)^3}\right]}-\frac{1}{3 a} \sqrt[3]{\tfrac12\left[2 b^3-9 a b c+27 a^2 d-\sqrt{\left(2 b^3-9 a b c+27 a^2 d\right)^2-4 \left(b^2-3 a c\right)^3}\right]}\\ &r_2 = -\frac{b}{3 a}+\frac{1+i \sqrt{3}}{6 a} \sqrt[3]{\tfrac12\left[2 b^3-9 a b c+27 a^2 d+\sqrt{\left(2 b^3-9 a b c+27 a^2 d\right)^2-4 \left(b^2-3 a c\right)^3}\right]}+\frac{1-i \sqrt{3}}{6 a} \sqrt[3]{\tfrac12\left[2 b^3-9 a b c+27 a^2 d-\sqrt{\left(2 b^3-9 a b c+27 a^2 d\right)^2-4 \left(b^2-3 a c\right)^3}\right]}\\ &r_3 = -\frac{b}{3 a}+\frac{1-i \sqrt{3}}{6 a} \sqrt[3]{\tfrac12\left[2 b^3-9 a b c+27 a^2 d+\sqrt{\left(2 b^3-9 a b c+27 a^2 d\right)^2-4 \left(b^2-3 a c\right)^3}\right]}+\frac{1+i \sqrt{3}}{6 a} \sqrt[3]{\tfrac12\left[2 b^3-9 a b c+27 a^2 d-\sqrt{\left(2 b^3-9 a b c+27 a^2 d\right)^2-4 \left(b^2-3 a c\right)^3}\right]}\\ &x^4+ax^3+bx^2+cx+d=0,\\

&r_1 = {\frac{-a}{4} - \frac{1}{2}{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} + \left(\frac {54}\right)^\frac{1}{3}}} - \frac{1}{2}{\sqrt{\frac{a^2}{2} - \frac{4b}{3} - \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} - \left(\frac {54}\right)^\frac{1}{3} - \frac{-a^3 + 4ab - 8c} {4{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}} \left( b^2 - 3ac + 12d \right) }{3 {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^ {\frac{1}{3}}} + \left( \frac{{ 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} } }{54}\right)^\frac{1}{3}}}}}}} \\ &r_2 = {\frac{-a}{4} - \frac{1}{2}{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} + \left( \frac {54}\right)^\frac{1}{3}}} + \frac{1}{2}{\sqrt{\frac{a^2}{2} - \frac{4b}{3} - \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} - \left( \frac {54}\right)^\frac{1}{3} - \frac{-a^3 + 4ab - 8c} {4{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}} \left( b^2 - 3ac + 12d \right) }{3 {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^ {\frac{1}{3}}} + \left( \frac{{ 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} } }{54}\right)^\frac{1}{3}}}}}}} \\ &r_3 = {\frac{-a}{4} + \frac{1}{2}{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} + \left( \frac {54}\right)^\frac{1}{3}}} - \frac{1}{2}{\sqrt{\frac{a^2}{2} - \frac{4b}{3} - \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} - \left( \frac {54}\right)^\frac{1}{3} + \frac{-a^3 + 4ab - 8c} {4{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}} \left( b^2 - 3ac + 12d \right) }{3 {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^ {\frac{1}{3}}} + \left( \frac{{ 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} } }{54}\right)^\frac{1}{3}}}}}}} \\ &r_4 = {\frac{-a}{4} + \frac{1}{2}{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} + \left( \frac {54}\right)^\frac{1}{3}}} + \frac{1}{2}{\sqrt{\frac{a^2}{2} - \frac{4b}{3} - \frac{2^{\frac{1}{3}}\left( b^2 - 3ac + 12d \right) } {3{\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4{\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^{\frac{1}{3}}} - \left( \frac {54} \right)^\frac{1}{3} + \frac{-a^3 + 4ab - 8c} {4{\sqrt{\frac{a^2}{4} - \frac{2b}{3} + \frac{2^{\frac{1}{3}} \left( b^2 - 3ac + 12d \right) }{3 {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} \right) }^ {\frac{1}{3}}} + \left( \frac{{ 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd + {\sqrt{-4 {\left( b^2 - 3ac + 12d \right) }^3 + {\left( 2b^3 - 9abc + 27c^2 + 27a^2d - 72bd \right) }^2}} } }{54}\right)^\frac{1}{3}}}}}}} \end{align}$$