SOLUTION: 3x^2+12x+8=0

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Question 83030: 3x^2+12x+8=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To solve for x we can use the quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B12x%2B8+=+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=%2812%29%5E2-4%2A3%2A8=48.

Discriminant d=48 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+48+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+48+%29%29%2F2%5C3+=+-0.845299461620749
x%5B2%5D+=+%28-%2812%29-sqrt%28+48+%29%29%2F2%5C3+=+-3.15470053837925

Quadratic expression 3x%5E2%2B12x%2B8 can be factored:
3x%5E2%2B12x%2B8+=+3%28x--0.845299461620749%29%2A%28x--3.15470053837925%29
Again, the answer is: -0.845299461620749, -3.15470053837925. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B12%2Ax%2B8+%29