数学公式压力测试

四次方程求根公式，搬运自数学史上你认为最丑陋的公式是什么？——知乎

$a{x}^4+b{x}^3+c{x}^2+dx+e=0,a,b,c,d,e\in \mathbb{R},a\ne 0$，则：

$$x_1=\frac{-b}{4a}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}-(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})-\frac{-\frac{b^3}{a^3}+\frac{4bc}{a^2}-\frac{8d}{a}}{4\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}}}$$$$x_2=\frac{-b}{4a}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}+\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}-(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})-\frac{-\frac{b^3}{a^3}+\frac{4bc}{a^2}-\frac{8d}{a}}{4\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}}}$$$$x_3=\frac{-b}{4a}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}-(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})+\frac{-\frac{b^3}{a^3}+\frac{4bc}{a^2}-\frac{8d}{a}}{4\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}}}$$$$x_4=\frac{-b}{4a}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}+\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}-(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})+\frac{-\frac{b^3}{a^3}+\frac{4bc}{a^2}-\frac{8d}{a}}{4\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+(\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}+\frac{\sqrt[3]{(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace)+\sqrt{-4(c^2-3bd+12ae{)}^3+(2c^3-9bcd+27a{d}^2+27b^{2}e-72ace{)}^2}}}{3\sqrt[3]{2}a})}}}$$