The breakeven point is the point where there is no profit and no deficit. In other words, the poitns when . You find x values of this by finding the roots of the equation. Using the quadratic formula!

or

For the maximum, the first derivative of the function is 0. Solve for x, and then plug that x value into the original equation to find P(x) for that value of x. The 2nd derivative test will tell you whether you have a maximum or a minimum. (Although you will have a maximum, since your coefficients of x^2 is negative!)