Quadratic Equation And Inequalities

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 __________.