The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7192\\[1 em]x_2 &= -2.7808 \end{aligned} $$The solutions of $ 2x^2+7x+4 = 0 $ are: $ x = -\dfrac{ 7 }{ 4 }-\dfrac{\sqrt{ 17 }}{ 4 } ~ \text{and} ~ x = -\dfrac{ 7 }{ 4 }+\dfrac{\sqrt{ 17 }}{ 4 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.