SOLUTION: How do I solve for x in this equation? 12x^2 + 21x + 6 = 0

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Question 311357: How do I solve for x in this equation?
12x^2 + 21x + 6 = 0
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
factor out a 3
3%286x%5E2%2B7x%2B2%29=0
use the quadratic formula to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B7x%2B2+=+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=%287%29%5E2-4%2A6%2A2=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+1+%29%29%2F2%5C6+=+-0.5
x%5B2%5D+=+%28-%287%29-sqrt%28+1+%29%29%2F2%5C6+=+-0.666666666666667

Quadratic expression 6x%5E2%2B7x%2B2 can be factored:
6x%5E2%2B7x%2B2+=+6%28x--0.5%29%2A%28x--0.666666666666667%29
Again, the answer is: -0.5, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B7%2Ax%2B2+%29