$\left\{\begin{matrix}a=-\frac{x\left(x+2b\right)}{4c}\text{, }&\left(x+b\geq 0\text{ and }c\neq 0\text{ and }b\leq -\sqrt{-x\left(x+2b\right)}\text{ and }x\geq -2b\text{ and }x\leq 0\right)\text{ or }\left(c\neq 0\text{ and }x=-2b\text{ and }b\leq 0\right)\text{ or }\left(x+b\geq 0\text{ and }c\neq 0\text{ and }b\leq -\sqrt{-x\left(x+2b\right)}\text{ and }x\geq 0\text{ and }x\leq -2b\right)\text{ or }\left(x+b\geq 0\text{ and }c\neq 0\text{ and }x>-2b\right)\\a\in \mathrm{R}\text{, }&\left(x=0\text{ and }c=0\text{ and }b\geq 0\right)\text{ or }\left(x=-2b\text{ and }c=0\text{ and }b\leq 0\right)\end{matrix}\right.$

$\left\{\begin{matrix}a=-\frac{x\left(x+2b\right)}{4c}\text{, }&c\neq 0\text{ and }\left(x=-b\text{ or }arg(x+b)<\pi \right)\\a\in \mathrm{C}\text{, }&\left(arg(b)<\pi \text{ or }x=-2b\right)\text{ and }\left(arg(b)\geq \pi \text{ or }x=0\right)\text{ and }\left(x=0\text{ or }x=-2b\right)\text{ and }c=0\end{matrix}\right.$

$\left\{\begin{matrix}b=-\frac{2ac}{x}-\frac{x}{2}\text{, }&x\neq 0\text{ and }arg(x+b)<\pi \\b\in \mathrm{C}\text{, }&\left(a=0\text{ or }c=0\right)\text{ and }x=0\text{ and }arg(b)<\pi \\b=-x\text{, }&x=-2\sqrt{a}\sqrt{c}\text{ or }x=2\sqrt{a}\sqrt{c}\end{matrix}\right.$