The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -17.2625\\[1 em]x_2 &= -702.7375 \end{aligned} $$The solutions of $ x^2+720x+12131 = 0 $ are: $ x = -360-\sqrt{ 117469 } ~ \text{and} ~ x = -360+\sqrt{ 117469 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.