Question

The profit (p) in dollars, for a company is modeled by the function p(x)=-7520x^2 +15000x, where x is the number of items produced. For which value of x will the company loss?

Answer 1

Well P(x) is the total money they made. 

so if P(X) < 0 they had a loss. 

so if you plug in 0 you get

0=-7520x^2+15000x
add 7520x^2 to both sides

7520x^2=15000x

(7520x)x is the same thing, if you multiply it out it will still equal 7520x^2

so (7520x)x=15,000x

divide both sides by x and

7520x=15,000

divide both sides by 7520

x=1.995

then you would just need to check a number on both sides, 

i.e. 0 and 2

2 gives you a value of -80 which means anything greater then 1.995 would be negative