Skylar repairs microwaves her revenue equals r(h)=80+30h for every h hour she spends repairing microwaves. her overhead costs c(h)=10h2-20, after how many hours does she break even

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:




And then solve for h:

We can solve with the quadratic formula, or more easily, by factoring:

So either
           OR            
                                     

Since a negative number of hours makes no sense:  h=5.

She will break even after 5 hours.