Maximize difference between bounds

This might be long/hard to follow but ill try my best to make the question clear:

We have a function C =int(from a to b) (7x-x² -10)dx

How can we pick the constants a and b such that C=0 and maximize (b-a)? a<b

I have tried and tried again but i just cannot come up with the correct answer, only answers that seem logical but are flat out wrong. In some cases i just get a long and tedious cubic function with two variables, trying to find when it equals 0. I know there is probably some neat trick to save all the calculations but i cant come up with one.