Dave's revenue $R on the sale of widgets is determined by the formula
R = 35x - x^2
His cost $C for producing x widgets is given by the formula C = 5x + 30. For what values of x is Dave's profit positive?
You need to determine the values of x for which C = 5x + 30 is less than R = 35x - x^2. The critical values of x for which C=R are the solutions to 35x - x^2 = 5x + 30, or x^2 - 30x + 30 = 0: these are 15 +- sqrt(195) or approximately 28.96 and 1.04. Since x has to be an integer the range of values for which C is less than R is 2 <= x <= 28.