Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{\sqrt{10}\left(-\frac{1}{20}+\frac{1}{20}i\right)\sqrt[4]{-\sqrt{10}A-2\sqrt[6]{2000}}}{gt}\text{; }a=\frac{\sqrt{10}\left(\frac{1}{20}+\frac{1}{20}i\right)\sqrt[4]{-\sqrt{10}A-2\sqrt[6]{2000}}}{gt}\text{; }a=\frac{\sqrt{10}\left(-\frac{1}{20}-\frac{1}{20}i\right)\sqrt[4]{-\sqrt{10}A-2\sqrt[6]{2000}}}{gt}\text{; }a=\frac{\sqrt{10}\left(\frac{1}{20}-\frac{1}{20}i\right)\sqrt[4]{-\sqrt{10}A-2\sqrt[6]{2000}}}{gt}\text{, }&g\neq 0\text{ and }t\neq 0\\a\in \mathrm{C}\text{, }&A=-2\sqrt[6]{2}\text{ and }\left(g=0\text{ or }t=0\right)\end{matrix}\right.
Solve for A
A=40\sqrt{10}\left(agt\right)^{4}-2^{\frac{7}{6}}
Solve for a
\left\{\begin{matrix}a=0\text{, }&A=-2\sqrt[6]{2}\text{ and }g\neq 0\text{ and }t\neq 0\\a=\frac{\sqrt{5}\sqrt[4]{\sqrt{10}A+2\sqrt[6]{2000}}}{10gt}\text{; }a=-\frac{\sqrt{5}\sqrt[4]{\sqrt{10}A+2\sqrt[6]{2000}}}{10gt}\text{, }&A\geq -2\sqrt[6]{2}\text{ and }g\neq 0\text{ and }t\neq 0\\a\in \mathrm{R}\text{, }&A=-2\sqrt[6]{2}\text{ and }\left(g=0\text{ or }t=0\right)\end{matrix}\right.
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