Math Problem Solver

$$\begin{aligned}x &= \begin{cases} - \frac{\sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}{2} - \frac{\sqrt{\sqrt[3]{- \frac{b^{2}}{a^{2}}} + \frac{2 b}{a \sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}}}{2} & \text{for}\: \frac{c}{a} = 0 \\- \frac{\sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} + \frac{2 b}{a \sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}} + \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} & \text{otherwise} \end{cases}\\x &= \begin{cases} - \frac{\sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}{2} + \frac{\sqrt{\sqrt[3]{- \frac{b^{2}}{a^{2}}} + \frac{2 b}{a \sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}}}{2} & \text{for}\: \frac{c}{a} = 0 \\- \frac{\sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} + \frac{2 b}{a \sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}} + \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} & \text{otherwise} \end{cases}\\x &= \begin{cases} \frac{\sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}{2} - \frac{\sqrt{\sqrt[3]{- \frac{b^{2}}{a^{2}}} - \frac{2 b}{a \sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}}}{2} & \text{for}\: \frac{c}{a} = 0 \\\frac{\sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 b}{a \sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}} + \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} & \text{otherwise} \end{cases}\\x &= \begin{cases} \frac{\sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}{2} + \frac{\sqrt{\sqrt[3]{- \frac{b^{2}}{a^{2}}} - \frac{2 b}{a \sqrt{- \sqrt[3]{- \frac{b^{2}}{a^{2}}}}}}}{2} & \text{for}\: \frac{c}{a} = 0 \\\frac{\sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 b}{a \sqrt{2 \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}} - \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}} + \frac{2 c}{3 a \sqrt[3]{\sqrt{\frac{c^{3}}{27 a^{3}} + \frac{b^{4}}{256 a^{4}}} + \frac{b^{2}}{16 a^{2}}}}}}{2} & \text{otherwise} \end{cases}\end{aligned}$$