SOLUTION: 3x^2+19x=154

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Question 606890: 3x^2+19x=154
Answer by asuar010(338) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B19x%2B-154+=+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=%2819%29%5E2-4%2A3%2A-154=2209.

Discriminant d=2209 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-19%2B-sqrt%28+2209+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2819%29%2Bsqrt%28+2209+%29%29%2F2%5C3+=+4.66666666666667
x%5B2%5D+=+%28-%2819%29-sqrt%28+2209+%29%29%2F2%5C3+=+-11

Quadratic expression 3x%5E2%2B19x%2B-154 can be factored:
3x%5E2%2B19x%2B-154+=+3%28x-4.66666666666667%29%2A%28x--11%29
Again, the answer is: 4.66666666666667, -11. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B19%2Ax%2B-154+%29