The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 18.9818\\[1 em]x_2 &= -2.9818 \end{aligned} $$The solutions of $ 5x^2-80x-283 = 0 $ are: $ x = 8-\dfrac{ 3 \sqrt{ 335}}{ 5 } ~ \text{and} ~ x = 8+\dfrac{ 3 \sqrt{ 335}}{ 5 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.