SOLUTION: 15x=(x+4)(2x-6)

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Question 40748: 15x=(x+4)(2x-6)
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
15x+=+%28x%2B4%29%282x-6%29
15x+=+2x%5E2+%2B+8x+-+6x+-+24
0+=+2x%5E2+-+13x+-+24
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-13x%2B-24+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-13%29%5E2-4%2A2%2A-24=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+361+%29%29%2F2%5C2+=+8
x%5B2%5D+=+%28-%28-13%29-sqrt%28+361+%29%29%2F2%5C2+=+-1.5

Quadratic expression 2x%5E2%2B-13x%2B-24 can be factored:
2x%5E2%2B-13x%2B-24+=+2%28x-8%29%2A%28x--1.5%29
Again, the answer is: 8, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-13%2Ax%2B-24+%29