Question

$$y=\frac{3x^{2}}{(2x-1)^{2}}$$

Solve for x (complex solution)

$\left\{\begin{matrix}x=\frac{\sqrt{y}\left(-2\sqrt{y}+\sqrt{3}\right)}{3-4y}\text{; }x=\frac{\sqrt{y}}{2\sqrt{y}-\sqrt{3}}\text{, }&y\neq \frac{3}{4}\\x=\frac{1}{4}=0.25\text{, }&y=\frac{3}{4}\end{matrix}\right.$

Solve for x

$\left\{\begin{matrix}x=\frac{\sqrt{y}\left(-2\sqrt{y}+\sqrt{3}\right)}{3-4y}\text{; }x=\frac{\sqrt{y}}{2\sqrt{y}-\sqrt{3}}\text{, }&y\neq \frac{3}{4}\text{ and }y\geq 0\\x=\frac{1}{4}=0.25\text{, }&y=\frac{3}{4}\end{matrix}\right.$

Solve for y

$y=3\times \left(\frac{x}{2x-1}\right)^{2}$
$x\neq \frac{1}{2}$