SOLUTION: 7/x+2 + 12=8/x-2

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Question 158885: 7/x+2 + 12=8/x-2
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
7/x+2 + 12=8/x-2
7(x-2)+12(x-2)(x+2)=8(x+2) multiply each side by the LCM to eliminate fractions.
7x-14+12(x^2-4)=8x+16
7x-14+12x^2-48=8x+16
12x^2-x-78=0
x=-2.50518..., x=2.59152... see below
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-1x%2B-78+=+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=%28-1%29%5E2-4%2A12%2A-78=3745.

Discriminant d=3745 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+3745+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+3745+%29%29%2F2%5C12+=+2.59151688013237
x%5B2%5D+=+%28-%28-1%29-sqrt%28+3745+%29%29%2F2%5C12+=+-2.50818354679904

Quadratic expression 12x%5E2%2B-1x%2B-78 can be factored:
12x%5E2%2B-1x%2B-78+=+%28x-2.59151688013237%29%2A%28x--2.50818354679904%29
Again, the answer is: 2.59151688013237, -2.50818354679904. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-1%2Ax%2B-78+%29