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