The roots of polynomial $ p(k) $ are:
$$ \begin{aligned}k_1 &= 14.8977\\[1 em]k_2 &= 0.6719 \end{aligned} $$The solutions of $ 999k^2-15554k+10000 = 0 $ are: $ k = \dfrac{ 7777 }{ 999 }-\dfrac{\sqrt{ 50491729 }}{ 999 } ~ \text{and} ~ k = \dfrac{ 7777 }{ 999 }+\dfrac{\sqrt{ 50491729 }}{ 999 }$.
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