SOLUTION: 6/x^2 - 29/x = 17. Can anyone explain to me how to do this step by step?

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Question 262602: 6/x^2 - 29/x = 17. Can anyone explain to me how to do this step by step?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
6/x^2 - 29/x = 17
Eliminate the fractions by multiplying by x^2
6 - 29x = 17x^2
17x^2 + 29x - 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 17x%5E2%2B29x%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=%2829%29%5E2-4%2A17%2A-6=1249.

Discriminant d=1249 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-29%2B-sqrt%28+1249+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2829%29%2Bsqrt%28+1249+%29%29%2F2%5C17+=+0.186505708651311
x%5B2%5D+=+%28-%2829%29-sqrt%28+1249+%29%29%2F2%5C17+=+-1.89238806159249

Quadratic expression 17x%5E2%2B29x%2B-6 can be factored:
17x%5E2%2B29x%2B-6+=+%28x-0.186505708651311%29%2A%28x--1.89238806159249%29
Again, the answer is: 0.186505708651311, -1.89238806159249. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+17%2Ax%5E2%2B29%2Ax%2B-6+%29