The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.428\\[1 em]x_2 &= -0.564+1.1369i\\[1 em]x_3 &= -0.564-1.1369i \end{aligned} $$Polynomial $ 10x^3-3x^2-23 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.