Solve for k
\left\{\begin{matrix}k=-\frac{\sqrt{\frac{y+2\sqrt{25-6y}-6}{4-y}}}{2}\text{; }k=\frac{\sqrt{\frac{y+2\sqrt{25-6y}-6}{4-y}}}{2}\text{, }&y\geq -16\text{ and }y\neq 4\text{ and }y\leq \frac{25}{6}\\k=-\frac{\sqrt{-\frac{-y+2\sqrt{25-6y}+6}{4-y}}}{2}\text{; }k=\frac{\sqrt{-\frac{-y+2\sqrt{25-6y}+6}{4-y}}}{2}\text{, }&y>4\text{ and }y\leq \frac{25}{6}\\k=\frac{\sqrt{5}}{2}\text{; }k=-\frac{\sqrt{5}}{2}\text{, }&y=4\end{matrix}\right.
Solve for y
y=-\frac{16\left(1-3k^{2}-4k^{4}\right)}{\left(4k^{2}+1\right)^{2}}
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