The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -5.5858\\[1 em]x_2 &= -8.4142 \end{aligned} $$The solutions of $ x^2+14x+47 = 0 $ are: $ x = -7-\sqrt{ 2 } ~ \text{and} ~ x = -7+\sqrt{ 2 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.