Let a, b, c be the lengths of three sides of a triangle satistying the condition (a^2+b^2) x^2-2 b(a+c) x+(b^2+c^2)=0. If the set of all possible…

Let $\displaystyle a, b, c$ be the lengths of three sides of a triangle satistying the condition $\displaystyle \left(a^2+b^2\right) x^2-2 b(a+c) x+\left(b^2+c^2\right)=0$. If the set of all possible values of $\displaystyle x$ is the interval $\displaystyle (\alpha, \beta)$, then $\displaystyle 12\left(\alpha^2+\beta^2\right)$ is equal to $\displaystyle \_\_\_\_$.