The root of polynomial $ p(x) $ is:
$$ \begin{aligned}x &= \frac{ 3 }{ 2 } \end{aligned} $$The solution of $ ~ 12x^2-36x+27 = 0 ~$ is $~ x = \dfrac{ 3 }{ 2 } ~$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.