Start with your first step. Solve for c via the quadratic formula (or factoring if it's possible).
I don't think you'll end up with an inverse function though...P(c) is not bijective.
The two values I got for c were 30 and 80. P(c) represents the daily profit earned as related to the number of cases, c, produced and sold. I have to find a function that gives the number of cases based on the profit desired. Wouldn't that be the inverse function?
You need to subtract P from both sides first:
Now you can do the quadratic equation with a=-1, b=110, and c=-2400-P (that's c in the quadratic equation, not c the number of cases).
What richard1234 is saying is that when you write out the quadratic equation, you get two solutions (because of the + or -), and you can't have a function with two outputs for the same input. You need more information to figure out which is correct, + or -.
Sometimes in problems like this, the "-" solution ends up being physically impossible - like the number of cases being negative. I don't think that happens in your problem, though.