Solve for a
a=-\sqrt{x^{6}+1200}+35
a=\sqrt{x^{6}+1200}+35\text{, }x\geq 0
Solve for x
\left\{\begin{matrix}x=\sqrt[6]{a^{2}-70a+25}\text{, }&a\geq 20\sqrt{3}+35\text{ or }a\leq 35-20\sqrt{3}\\x=\frac{2^{\frac{2}{3}}\sqrt[3]{-\sqrt{a^{2}-70a+25}+\sqrt{-3a^{2}+210a-75}}}{2}\text{; }x=\frac{2^{\frac{2}{3}}\sqrt[3]{-\sqrt{a^{2}-70a+25}-\sqrt{-3a^{2}+210a-75}}}{2}\text{, }&a=35-20\sqrt{3}\text{ or }a=20\sqrt{3}+35\end{matrix}\right.
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