Question 108
Find all real numbers $a$ for which the equation $x^{2}+a x+3 a^{2}-7 a-19=0$ has real roots $x_{1}$ and $x_{2}$ such that
$$
\frac{1}{x_{1}-2}+\frac{1}{x_{2}-2}=-\frac{2 a}{13}
$$
$$
\frac{1}{x_{1}-2}+\frac{1}{x_{2}-2}=-\frac{2 a}{13}
$$