$$(a-b)x^{2}+(b-c)x+(c-a)=0; T_{0}; 2a=b+c$$
$\left\{\begin{matrix}x=1\text{, }&d=T_{0}\\x=-\frac{c-a}{b-a}\text{, }&a\neq b\text{ and }d=T_{0}\\x\in \mathrm{C}\text{, }&c=b\text{ and }a=b\text{ and }d=T_{0}\end{matrix}\right.$
$\left\{\begin{matrix}x=1\text{, }&d=T_{0}\\x=-\frac{c-a}{b-a}\text{, }&a\neq b\text{ and }d=T_{0}\\x\in \mathrm{R}\text{, }&c=b\text{ and }a=b\text{ and }d=T_{0}\end{matrix}\right.$
