Solve {c}{y=ax^2-4ax+3a}{x=2quady=3}

$$\left. \begin{array} { c } { y = a x ^ { 2 } - 4 a x + 3 a } \\ { x = 2 \quad y = 3 } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{16a^{2}+16a+1}-8a-1}{4a}\text{, }y=-\frac{\sqrt{16a^{2}+16a+1}-8a-1}{8a}\text{; }x=\frac{\sqrt{16a^{2}+16a+1}+8a+1}{4a}\text{, }y=\frac{\sqrt{16a^{2}+16a+1}+8a+1}{8a}\text{, }&a\neq 0\\x=0\text{, }y=0\text{, }&a=0\end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}x=-\frac{\sqrt{16a^{2}+16a+1}-8a-1}{4a}\text{, }y=-\frac{\sqrt{16a^{2}+16a+1}-8a-1}{8a}\text{; }x=\frac{\sqrt{16a^{2}+16a+1}+8a+1}{4a}\text{, }y=\frac{\sqrt{16a^{2}+16a+1}+8a+1}{8a}\text{, }&a\leq -\frac{\sqrt{3}}{4}-\frac{1}{2}\text{ or }\left(a\neq 0\text{ and }a\geq \frac{\sqrt{3}}{4}-\frac{1}{2}\right)\\x=0\text{, }y=0\text{, }&a=0\end{matrix}\right.$$