SOLUTION: Can someone please provide me with a breakdown of how to solve this problem? Thanks! x^2-5=12x

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Question 735861: Can someone please provide me with a breakdown of how to solve this problem? Thanks!
x^2-5=12x
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
subtract 12x
x^2-12x-5=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B-5+=+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=%28-12%29%5E2-4%2A1%2A-5=164.

Discriminant d=164 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+164+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+164+%29%29%2F2%5C1+=+12.4031242374328
x%5B2%5D+=+%28-%28-12%29-sqrt%28+164+%29%29%2F2%5C1+=+-0.403124237432849

Quadratic expression 1x%5E2%2B-12x%2B-5 can be factored:
1x%5E2%2B-12x%2B-5+=+%28x-12.4031242374328%29%2A%28x--0.403124237432849%29
Again, the answer is: 12.4031242374328, -0.403124237432849. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B-5+%29