Solve y=|2/n-3*sqrt{|1/2x+2|}|

$$y = | \frac { 2 } { n } - 3 \cdot \sqrt { | \frac { 1 } { 2 } x + 2 | } |$$

Solve for n

$$\left\{\begin{matrix}n=\frac{2}{y+3\sqrt{|\frac{x+4}{2}|}}\text{, }&y\neq -3\sqrt{|\frac{x}{2}+2|}\text{ and }y\geq 0\\n=-\frac{2}{y-3\sqrt{|\frac{x+4}{2}|}}\text{, }&y\neq 3\sqrt{|\frac{x}{2}+2|}\text{ and }y\geq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2y^{2}}{9}-\frac{8y}{9n}-4+\frac{8}{9n^{2}}\text{; }x=-\frac{2y^{2}}{9}+\frac{8y}{9n}-4-\frac{8}{9n^{2}}\text{, }&-\frac{y}{3}+\frac{2}{3n}\geq 0\text{ and }n\neq 0\text{ and }y\geq 0\\x=\frac{2y^{2}}{9}+\frac{8y}{9n}-4+\frac{8}{9n^{2}}\text{; }x=-\frac{2y^{2}}{9}-\frac{8y}{9n}-4-\frac{8}{9n^{2}}\text{, }&\frac{y}{3}+\frac{2}{3n}\geq 0\text{ and }n\neq 0\text{ and }y\geq 0\end{matrix}\right.$$