$x=\frac{1}{3iyf^{2}-1}$
$y=0\text{ or }\left(f\neq \left(-1+i\right)\times \left(6y\right)^{-\frac{1}{2}}\text{ and }f\neq \left(1-i\right)\times \left(6y\right)^{-\frac{1}{2}}\right)$

$\left\{\begin{matrix}f=\left(-\frac{1}{6}+\frac{1}{6}i\right)x^{-\frac{1}{2}}y^{-\frac{1}{2}}\sqrt{6\left(x+1\right)}\text{; }f=\left(\frac{1}{6}-\frac{1}{6}i\right)x^{-\frac{1}{2}}y^{-\frac{1}{2}}\sqrt{6\left(x+1\right)}\text{, }&y\neq 0\text{ and }x\neq 0\\f\in \mathrm{C}\text{, }&x=-1\text{ and }y=0\end{matrix}\right.$