SOLUTION: solve quadratic equation x^2=6x-3

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Question 191715: solve quadratic equation
x^2=6x-3
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
x^2=6x-3
Move all terms to the left:
x^2-6x+3 = 0
Since we can't factor, we must resort to the quadratic equation.
Doing so, yields two solutions:
x = {5.449, 0.551}
.
Details of quadratic equation follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B3+=+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=%28-6%29%5E2-4%2A1%2A3=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+24+%29%29%2F2%5C1+=+5.44948974278318
x%5B2%5D+=+%28-%28-6%29-sqrt%28+24+%29%29%2F2%5C1+=+0.550510257216822

Quadratic expression 1x%5E2%2B-6x%2B3 can be factored:
1x%5E2%2B-6x%2B3+=+1%28x-5.44948974278318%29%2A%28x-0.550510257216822%29
Again, the answer is: 5.44948974278318, 0.550510257216822. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B3+%29