The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= 1.2374\\[1 em]t_2 &= -0.4041 \end{aligned} $$The solutions of $ 12t^2-10t-6 = 0 $ are: $ t = \dfrac{ 5 }{ 12 }-\dfrac{\sqrt{ 97 }}{ 12 } ~ \text{and} ~ t = \dfrac{ 5 }{ 12 }+\dfrac{\sqrt{ 97 }}{ 12 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.