The roots of polynomial $ p(n) $ are:
$$ \begin{aligned}n_1 &= 148.1206\\[1 em]n_2 &= -648.1206 \end{aligned} $$The solutions of $ n^2+500n-96000 = 0 $ are: $ n = -250-10 \sqrt{ 1585 } ~ \text{and} ~ n = -250+10 \sqrt{ 1585 }$.
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