The root of polynomial $ p(x) $ is:
$$ \begin{aligned}x &= -\dfrac{ 4 }{ 3 } \end{aligned} $$The solution of $ ~ -9x^2-24x-16 = 0 ~$ is $~ x = -\dfrac{ 4 }{ 3 } ~$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.