SOLUTION: I'm working on proportions. I solved the proportion part and got 6x squared plus 12 equals -38x and I'm lost from there. How do you get the answer from there?

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Question 447628: I'm working on proportions. I solved the proportion part and got 6x squared plus 12 equals -38x and I'm lost from there. How do you get the answer from there?
Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
6x squared plus 12 equals -38x
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3x%5E2+%2B+19x+%2B+6+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B19x%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=%2819%29%5E2-4%2A3%2A6=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-19%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2819%29%2Bsqrt%28+289+%29%29%2F2%5C3+=+-0.333333333333333
x%5B2%5D+=+%28-%2819%29-sqrt%28+289+%29%29%2F2%5C3+=+-6

Quadratic expression 3x%5E2%2B19x%2B6 can be factored:
3x%5E2%2B19x%2B6+=+%28x--0.333333333333333%29%2A%28x--6%29
Again, the answer is: -0.333333333333333, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B19%2Ax%2B6+%29