The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.4506\\[1 em]x_2 &= 1.5566+1.1421i\\[1 em]x_3 &= 1.5566-1.1421i\\[1 em]x_4 &= -3.1153+2.5237i\\[1 em]x_5 &= -3.1153-2.5237i \end{aligned} $$Polynomial $ 3x^5+8x^4-3x^3-81x^2+216x-81 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.