SOLUTION: Solve: y-1/y+7=2/7

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Question 296258: Solve:
y-1/y+7=2/7
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
multiply by 7y
7y^2-7+49y=2y
7y^2+47y-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 7y%5E2%2B47y%2B-7+=+0) has the following solutons:

y%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=%2847%29%5E2-4%2A7%2A-7=2405.

Discriminant d=2405 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-47%2B-sqrt%28+2405+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%2847%29%2Bsqrt%28+2405+%29%29%2F2%5C7+=+0.145771381496923
y%5B2%5D+=+%28-%2847%29-sqrt%28+2405+%29%29%2F2%5C7+=+-6.86005709578264

Quadratic expression 7y%5E2%2B47y%2B-7 can be factored:
7y%5E2%2B47y%2B-7+=+7%28y-0.145771381496923%29%2A%28y--6.86005709578264%29
Again, the answer is: 0.145771381496923, -6.86005709578264. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B47%2Ax%2B-7+%29