SOLUTION: solve: 3+1/x-2=2x-3/x-2

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Question 35587: solve:
3+1/x-2=2x-3/x-2
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
3+(1/x-2)=2x-(3/x-2) original
(x-2)(3+(1/x-2))=(x-2)(2x-(3/x-2))
3x-6+1=2x^2-4x-3
0=2x^2-7x+2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-7x%2B2+=+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=%28-7%29%5E2-4%2A2%2A2=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+33+%29%29%2F2%5C2+=+3.18614066163451
x%5B2%5D+=+%28-%28-7%29-sqrt%28+33+%29%29%2F2%5C2+=+0.313859338365493

Quadratic expression 2x%5E2%2B-7x%2B2 can be factored:
2x%5E2%2B-7x%2B2+=+2%28x-3.18614066163451%29%2A%28x-0.313859338365493%29
Again, the answer is: 3.18614066163451, 0.313859338365493. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-7%2Ax%2B2+%29