The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 7.8934\\[1 em]x_2 &= -13.8934 \end{aligned} $$The solutions of $ 3x^2+18x-329 = 0 $ are: $ x = -3-\dfrac{ 2 \sqrt{ 267}}{ 3 } ~ \text{and} ~ x = -3+\dfrac{ 2 \sqrt{ 267}}{ 3 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.