Solve 1/4=(2k+2)^2-(gamma-k)^2/(8-k)^2

$$\frac { 1 } { 4 } = \frac { ( 2 k + 2 ) ^ { 2 } - ( \gamma - k ) ^ { 2 } } { ( 8 - k ) ^ { 2 } }$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=\frac{-2\sqrt{15\gamma ^{2}+48\gamma +276}-4\gamma -24}{11}\text{, }&\text{unconditionally}\\k=\frac{2\sqrt{15\gamma ^{2}+48\gamma +276}-4\gamma -24}{11}\text{, }&\gamma \neq -10\text{ and }\gamma \neq 26\end{matrix}\right.$$

Solve for γ (complex solution)

$$\gamma =\frac{\sqrt{15k-12}\sqrt{k+4}}{2}+k$$

$$\gamma =-\frac{\sqrt{5k-4}\sqrt{3k+12}}{2}+k\text{, }k\neq 8$$

Solve for k

$$\left\{\begin{matrix}\\k=\frac{-2\sqrt{15\gamma ^{2}+48\gamma +276}-4\gamma -24}{11}\text{, }&\text{unconditionally}\\k=\frac{2\sqrt{15\gamma ^{2}+48\gamma +276}-4\gamma -24}{11}\text{, }&\gamma \neq 26\text{ and }\gamma \neq -10\end{matrix}\right.$$

Solve for γ

$$\left\{\begin{matrix}\gamma =-\frac{\sqrt{15k^{2}+48k-48}}{2}+k\text{; }\gamma =\frac{\sqrt{15k^{2}+48k-48}}{2}+k\text{, }&k\geq \frac{4}{5}\text{ and }k\neq 8\\\gamma =-\frac{\sqrt{15k^{2}+48k-48}}{2}+k\text{; }\gamma =\frac{\sqrt{15k^{2}+48k-48}}{2}+k\text{, }&k\leq -4\end{matrix}\right.$$