SOLUTION: I need help finding the answer to {{{2/(5x) + 1 = 1/3 + x}}}

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Question 542130: I need help finding the answer to 2%2F%285x%29+%2B+1+=+1%2F3+%2B+x
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%285x%29+%2B+1+=+1%2F3+%2B+x
2%2F%285x%29+%2B+3%2F3+=+1%2F3+%2B+x
2%2F%285x%29+%2B+2%2F3+=+x
%282%2F%285x%29%29%283%2A5x%29+%2B+2%2F3%283%2A5x%29+=+x%283%2A5x%29 multiply by common denom
6%2B10x=15x%5E2 put in quadratic equation form
0=15x%5E2-10x-6 solve quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B-10x%2B-6+=+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=%28-10%29%5E2-4%2A15%2A-6=460.

Discriminant d=460 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+460+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+460+%29%29%2F2%5C15+=+1.04825368631757
x%5B2%5D+=+%28-%28-10%29-sqrt%28+460+%29%29%2F2%5C15+=+-0.381587019650907

Quadratic expression 15x%5E2%2B-10x%2B-6 can be factored:
15x%5E2%2B-10x%2B-6+=+15%28x-1.04825368631757%29%2A%28x--0.381587019650907%29
Again, the answer is: 1.04825368631757, -0.381587019650907. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-10%2Ax%2B-6+%29