Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{25+150y+35y^{3}-240y^{4}-56y^{6}}+5}{8y^{3}-5}\text{; }x=\frac{-\sqrt{25+150y+35y^{3}-240y^{4}-56y^{6}}+5}{8y^{3}-5}\text{, }&y\neq \frac{\sqrt[3]{5}}{2}\text{ and }25+150y+35y^{3}-240y^{4}-56y^{6}\geq 0\\x=\frac{24\sqrt[3]{5}+7}{16}\text{, }&y=\frac{\sqrt[3]{5}}{2}\end{matrix}\right.
Solve for y
y=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{8x^{2}+7}x^{2}+\sqrt{8x^{6}+32x^{5}+39x^{4}+28x^{3}+28x^{2}+160}+2x\sqrt{8x^{2}+7}}+\sqrt[3]{\sqrt{8x^{2}+7}x^{2}-\sqrt{8x^{6}+32x^{5}+39x^{4}+28x^{3}+28x^{2}+160}+2x\sqrt{8x^{2}+7}}\right)}{2\sqrt{8x^{2}+7}}
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