Solve for K (complex solution)
\left\{\begin{matrix}K=-\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{; }K=\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{, }&a\neq 0\\K\in \mathrm{C}\text{, }&a=-1\end{matrix}\right.
Solve for a (complex solution)
\left\{\begin{matrix}\\a=-1\text{, }&\text{unconditionally}\\a=\frac{3}{16K^{2}+5}\text{, }&K\neq -\frac{\sqrt{5}i}{4}\text{ and }K\neq \frac{\sqrt{5}i}{4}\end{matrix}\right.
Solve for K
\left\{\begin{matrix}K=\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{; }K=-\frac{\sqrt{-5+\frac{3}{a}}}{4}\text{, }&a>0\text{ and }a\leq \frac{3}{5}\\K\in \mathrm{R}\text{, }&a=-1\end{matrix}\right.
Solve for a
a=-1
a=\frac{3}{16K^{2}+5}
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