The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 4.7417\\[1 em]x_2 &= -2.7417 \end{aligned} $$The solutions of $ x^2-2x-13 = 0 $ are: $ x = 1-\sqrt{ 14 } ~ \text{and} ~ x = 1+\sqrt{ 14 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.