find range and profit

Question

A cell phone company has the following cost and revenue functions: C(x) = 8x^2 - 600x + 21,500 and R(x) = -3x^2 + 480x. What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit.

Answer 1

-3x^2 + 480x - (8x^2 - 600x + 21500) > 0

-3x^2 + 480x - 8x^2 + 600x - 21500 > 0

-11x^2 + 1080x -21500 > 0

11x^2 - 1080x + 21500 < 0

quadratic formula says either more than 71 or at most 28;

between those two, there is loss