Solve y=x+x(4a)^6-4x

$$y = x + x ( 4 a ) ^ { 6 - 4 } x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{i\sqrt{x-y}}{4x}\text{; }a=\frac{i\sqrt{x-y}}{4x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{64ya^{2}+1}+1}{32a^{2}}\text{; }x=-\frac{-\sqrt{64ya^{2}+1}+1}{32a^{2}}\text{, }&a\neq 0\\x=y\text{, }&a=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\sqrt{y-x}}{4|x|}\text{; }a=-\frac{\sqrt{y-x}}{4|x|}\text{, }&y\geq x\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{64ya^{2}+1}+1}{32a^{2}}\text{; }x=-\frac{-\sqrt{64ya^{2}+1}+1}{32a^{2}}\text{, }&a\neq 0\text{ and }y\geq -\frac{1}{64a^{2}}\\x=y\text{, }&a=0\end{matrix}\right.$$