SOLUTION: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Mem

Question 433248: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Memphis.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
If Marty's speed is set equal to x, then:
270/x=(270/(x+15))+1.5
Multiply all by x(x+15), we get:
270(x+15)=270x+1.5(x2+15x)
270x+4050=270x+1.5x2+22.5x
0=1.5x2+22.5x-4050
Divide by 1.5:
0=x2+15x-2700
0=(x+60)(x-45)
x=-60,45
Throwing out the negative result, we get Marty's speed to Memphis as 45mph.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=11025 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 45, -60. Here's your graph:

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