The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.4501\\[1 em]x_2 &= -0.3988 \end{aligned} $$The solutions of $ -39x^2+2x+7 = 0 $ are: $ x = \dfrac{ 1 }{ 39 }-\dfrac{\sqrt{ 274 }}{ 39 } ~ \text{and} ~ x = \dfrac{ 1 }{ 39 }+\dfrac{\sqrt{ 274 }}{ 39 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.