$k=\frac{\sqrt{-\left(2x+3\right)x^{2}}+x}{x^{2}}$
$k=\frac{-\sqrt{-\left(2x+3\right)x^{2}}+x}{x^{2}}\text{, }x\neq 0$

$\left\{\begin{matrix}x=\frac{\sqrt{-\left(3k-1\right)\left(k+1\right)}+k-1}{k^{2}}\text{; }x=\frac{-\sqrt{-\left(3k-1\right)\left(k+1\right)}+k-1}{k^{2}}\text{, }&k\neq 0\\x=-2\text{, }&k=0\end{matrix}\right.$

$k=\frac{-\sqrt{-2x-3}+1}{x}$
$k=\frac{\sqrt{-2x-3}+1}{x}\text{, }x\leq -\frac{3}{2}$

$\left\{\begin{matrix}x=\frac{\sqrt{\left(1-3k\right)\left(k+1\right)}+k-1}{k^{2}}\text{; }x=\frac{-\sqrt{\left(1-3k\right)\left(k+1\right)}+k-1}{k^{2}}\text{, }&k\neq 0\text{ and }k\geq -1\text{ and }k\leq \frac{1}{3}\\x=-2\text{, }&k=0\end{matrix}\right.$