Find all solutions $x\in\Bbb R$ of the equation $$\sqrt{7x^2-22x+28}+\sqrt{7x^2+8x+13}+\sqrt{31x^2+14x+4}=5x+10.$$
My attempt: i substitute $$a=\sqrt{7x^2-22x+28} , \quad b=\sqrt{7x^2+8x+13} , \quad c=\sqrt{31x^2+14x+4}$$ then
$$a+b+c=5x+10, \quad a^2+b^2+c^2=-45x^2+5x-35.$$
But I don't know what to do next.