The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\frac{ 4 }{ 5 }\\[1 em]x_2 &= -1 \end{aligned} $$The solutions of $ 5x^2+9x+4 = 0 $ are: $ x = -1 ~ \text{and} ~ x = -\dfrac{ 4 }{ 5 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.