$\left\{\begin{matrix}A=-\frac{B-a-b}{3B+3YB^{2}+1}\text{, }&\left(B\neq -\frac{1}{3}\text{ and }B\neq \frac{\sqrt{9-12Y}-3}{6Y}\text{ and }B\neq -\frac{\sqrt{3}\left(\sqrt{3-4Y}+\sqrt{3}\right)}{6Y}\right)\text{ or }\left(B\neq -\frac{1}{3}\text{ and }Y=0\right)\text{ or }\left(Y\neq 0\text{ and }B\neq \frac{\sqrt{9-12Y}-3}{6Y}\text{ and }B\neq -\frac{\sqrt{3}\left(\sqrt{3-4Y}+\sqrt{3}\right)}{6Y}\right)\\A\in \mathrm{C}\text{, }&\left(B=-\frac{6Yb+\sqrt{9-12Y}+3}{6Y}+b\text{ and }a=-\frac{6Yb+\sqrt{9-12Y}+3}{6Y}\text{ and }Y\neq 0\right)\text{ or }\left(B=\frac{-6Yb+\sqrt{9-12Y}-3}{6Y}+b\text{ and }a=\frac{-6Yb+\sqrt{9-12Y}-3}{6Y}\text{ and }Y\neq 0\right)\text{ or }\left(B=-\frac{1}{3}\text{ and }a=-b-\frac{1}{3}\text{ and }Y=0\right)\end{matrix}\right.$

$\left\{\begin{matrix}B=\frac{\sqrt{9A^{2}+12AYa+12AYb+6A-12YA^{2}+1}-3A-1}{6AY}\text{; }B=-\frac{\sqrt{9A^{2}+12AYa+12AYb+6A-12YA^{2}+1}+3A+1}{6AY}\text{, }&Y\neq 0\text{ and }A\neq 0\\B=-\frac{A-a-b}{3A+1}\text{, }&A=0\text{ or }\left(Y=0\text{ and }A\neq -\frac{1}{3}\right)\\B\in \mathrm{C}\text{, }&Y=0\text{ and }A=-\frac{1}{3}\text{ and }a=-b-\frac{1}{3}\end{matrix}\right.$