To break even, means her revenue and overhead are equal, i.e. she isn't making any money but isn't losing any either. We can write an equation to represent this situation:
\(R(h)=C(h)\)
\(80+30h=10h^{2}-20\)
And then solve for h:
\(10h^{2}-30h-100=0\)
We can solve with the quadratic formula, or more easily, by factoring:
\(10(h-5)(h+2)=0\)
So either
\(h-5=0\) OR \(h+2=0\)
\(h=5\) \(h=-2\)
Since a negative number of hours makes no sense: h=5.
She will break even after 5 hours.
