SOLUTION: 2a^2-46a+254=0 thank you!

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Question 750575: 2a^2-46a+254=0 thank you!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2a^2-46a+254=0
first, divide both sides by 2:
a^2-23a+127=0
applying the "quadratic formula" yields:
a = {13.80, 9.21}
.
details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-23x%2B127+=+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=%28-23%29%5E2-4%2A1%2A127=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--23%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-23%29%2Bsqrt%28+21+%29%29%2F2%5C1+=+13.7912878474779
x%5B2%5D+=+%28-%28-23%29-sqrt%28+21+%29%29%2F2%5C1+=+9.20871215252208

Quadratic expression 1x%5E2%2B-23x%2B127 can be factored:
1x%5E2%2B-23x%2B127+=+1%28x-13.7912878474779%29%2A%28x-9.20871215252208%29
Again, the answer is: 13.7912878474779, 9.20871215252208. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-23%2Ax%2B127+%29