The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2538\\[1 em]x_2 &= -0.9295\\[1 em]x_3 &= -2.5742 \end{aligned} $$Polynomial $ -4x^3-9x^2+8x+12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.