$k=-\frac{3}{x\left(x-2\right)}$
$x\neq 2\text{ and }x\neq 0$

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

$x=\frac{\sqrt{k\left(k-3\right)}+k}{k}$
$x=\frac{-\sqrt{k\left(k-3\right)}+k}{k}\text{, }k<0\text{ or }k\geq 3$