The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -2\\[1 em]x_2 &= -\frac{ 5 }{ 2 } \end{aligned} $$The solutions of $ 2x^2+9x+10 = 0 $ are: $ x = -\dfrac{ 5 }{ 2 } ~ \text{and} ~ x = -2$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.