The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5636\\[1 em]x_2 &= -0.806\\[1 em]x_3 &= 2.7878+1.0166i\\[1 em]x_4 &= 2.7878-1.0166i \end{aligned} $$Polynomial $ 3x^4-16x^3+21x^2+14x-12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.