\begin{array}{l} {x_1=-\frac{b}{4a}+\frac{1}{2} \sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}}-\frac{1}{2} \sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}-\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}+\frac{-b^3+4abc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^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}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}}+\frac{1}{2} \sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}-\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}+\frac{-b^3+4abc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^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}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}}-\frac{1}{2} \sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}-\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}-\frac{-b^3+4abc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^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}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}}+\frac{1}{2} \sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}-\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}{3\sqrt[3]{2}a}-\frac{-b^3+4abc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{2c}{3a}+\frac{\sqrt[3]{2}\left(c^2-3bd+12ae\right)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4\left(c^2-3bd+12ae\right)^3+\left(2c^3-9bcd+27ad^2+27b^2e-72ace\right)^2}}} {3\sqrt[3]{2}a}}}}}\\\\ {\Delta=256a^3e^3-192a^2bde^2-128a^2c^2e^2+144a^2cd^2e-27a^2d^4+144ab^2ce^2-6ab^2d^2e-80abc^2de+18abcd^3+16ac^4e-4ac^3d^2-27b^4e^2+18b^3 c d e-4 b^3 d^3-4 b^2 c^3 e+b^2 c^2 d^2} \end{array}