SOLUTION: Solve the given equation. - 3/x + 10 = x - 10/25

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Question 158037: Solve the given equation.
- 3/x + 10 = x - 10/25
Answer by atique.ah(27) About Me  (Show Source):
You can put this solution on YOUR website!

- 3/x + 10 = x - 10/25
simplify
(x + 3/x) - 2/5 - 10=0
(x^2 + 3)/x - 52/5 = 0
5x^2 - 52x + 15 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-52x%2B15+=+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=%28-52%29%5E2-4%2A5%2A15=2404.

Discriminant d=2404 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--52%2B-sqrt%28+2404+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-52%29%2Bsqrt%28+2404+%29%29%2F2%5C5+=+10.1030602688525
x%5B2%5D+=+%28-%28-52%29-sqrt%28+2404+%29%29%2F2%5C5+=+0.296939731147495

Quadratic expression 5x%5E2%2B-52x%2B15 can be factored:
5x%5E2%2B-52x%2B15+=+5%28x-10.1030602688525%29%2A%28x-0.296939731147495%29
Again, the answer is: 10.1030602688525, 0.296939731147495. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-52%2Ax%2B15+%29