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