Help!! Please

Question

The monthly profit from producing and selling x units of a certain product is given by P(-x^2+320x-11200.
Producing and selling how many units will result in a profit for this product?
A. X<40 and x>280
B.x>0
C.0<x<320
D.40<x<280

Answer 1

-x^2 + 320x -11200= 0

x^2 -320x + 11200 = 0

x = 320/2 + (1/2)sqr(320^2 -4(11200))

= 160 +(1/2)sqr(102400 - 44800)

=160+ or - (1/2)sqr57600 = 160 + or -120 = 40 or 280

D) is correct 40<x<280