The roots of polynomial $ p(n) $ are:
$$ \begin{aligned}n_1 &= 18.2711\\[1 em]n_2 &= -26.2711 \end{aligned} $$The solutions of $ n^2+8n-480 = 0 $ are: $ n = -4-4 \sqrt{ 31 } ~ \text{and} ~ n = -4+4 \sqrt{ 31 }$.
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