SOLUTION: Use the quadratic formula to find exact solution: 3x squared plus 6 equals 10x

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Question 665031: Use the quadratic formula to find exact solution:
3x squared plus 6 equals 10x
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+%2B+6+=+10x
3x%5E2+-+10x+%2B+6+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-10x%2B6+=+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=%28-10%29%5E2-4%2A3%2A6=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+28+%29%29%2F2%5C3+=+2.54858377035486
x%5B2%5D+=+%28-%28-10%29-sqrt%28+28+%29%29%2F2%5C3+=+0.78474956297847

Quadratic expression 3x%5E2%2B-10x%2B6 can be factored:
3x%5E2%2B-10x%2B6+=+3%28x-2.54858377035486%29%2A%28x-0.78474956297847%29
Again, the answer is: 2.54858377035486, 0.78474956297847. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-10%2Ax%2B6+%29