The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7753\\[1 em]x_2 &= -3.2247 \end{aligned} $$The solutions of $ 2x^2+8x+5 = 0 $ are: $ x = -2-\dfrac{\sqrt{ 6 }}{ 2 } ~ \text{and} ~ x = -2+\dfrac{\sqrt{ 6 }}{ 2 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.