# Milestone: 100 day streak! (I just want to post a problem)

Geometry Level 5

$x^3-24x^2+180x-420=0$

A $\triangle ABC$ has sides $a,b$ and $c$. It is known that $a,b$ and $c$ are also the roots of the equation above.

Given that $\cos A+\cos B+\cos C =\dfrac{p}{q}$, where $p$ and $q$ are coprime positive integers, find the value of $11(p+q)+25$.

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