PLease help I know the answer is 34 but am lost at how to get it

Question

A theater company's annual profit is modeled by the equation P=0.2x^2-6.8x, Where X is the number of plays performed in a year.  How many plays must the company present in order to make a profit?  The answer 34 but please show how to understand. thank you

Answer 1

P = (0.2)x² - (6.)8x

 

The company makes a profit when P > 0 (or 0 < P)

 

0 < (0.2)x² - (6.8)x

 

6.8x < 0.2x²                    [Added 6.8x to both sides]

 

6.8 < 0.2x                   [Divided both sides by x]

 

34 < x                        [Divided both sides by 0.2]