Need help with cost function

Question

The cost function for a certain company is C = 30x + 600

 and the revenue is given by R = 100x − 0.5x².

 Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $600.

Answer 1

R-C = 600 = 100x - 0.5x^2 - (30x + 600) = -0.5x^2 + 70x -600

-0.5x^2 + 70x -1200 = 0 multiply by -1

x^2 -140x + 2400 = 0 factor

(x-20)(x-120) = 0

x = 20 or 120 = output levels that create $600 profit