The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.8473\\[1 em]x_2 &= -114.8473 \end{aligned} $$The solutions of $ -5x^2-560x+1635 = 0 $ are: $ x = -56-\sqrt{ 3463 } ~ \text{and} ~ x = -56+\sqrt{ 3463 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.