$$ax+b=x$$
$\left\{\begin{matrix}a=\frac{x-b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$
$\left\{\begin{matrix}a=\frac{x-b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$
$b=x\left(1-a\right)$