2(v+40)800+2(v-40)800=9(v+40)(v-40) solve using quadratics formula

Question

i need to solve this. The answer is v=360 or -4.44 repeating. I just do not know how to get there.

 

The original equation was 800 over v-40 + 800 over v+40 = 9 over 2

 

The original problem is... 

 

On a day w/ winds of 50mph, a plane flies round trip between two cities in 4.5 hours. If the cities are 800 miles apart, what is the planes speed in no wind?

Answer 1

Assuming that the velocity of the wind is 40 mph, 

 

800/(v+40) + 800/(v-40) = 9/2

 

Multiply by 2(v+40)(v-40):  

 

 1600(v-40)+1600(v+40) = 9(v+40)(v-40)

 

 3200v = 9(v² - 1600)

 

9v² - 3200v - 14400 = 0

 

v =   3200 ± √[(-3200² - 4(9)(-14400)]

                                  2(9)

 

   =    3200 ± √10758400 =  3200  ±  3280

                     18                                 18

 

                                            = 360, -4.444444

 

Since v can't be negative, v = 360 mph.