The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= 1.3097\\[1 em]s_2 &= 0.4357 \end{aligned} $$The solutions of $ 19958s^2-34834s+11388 = 0 $ are: $ s = \dfrac{ 17417 }{ 19958 }-\dfrac{\sqrt{ 76070185 }}{ 19958 } ~ \text{and} ~ s = \dfrac{ 17417 }{ 19958 }+\dfrac{\sqrt{ 76070185 }}{ 19958 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.