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

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Question 311298: How would I solve this equation for x?
12x^2 + 21x + 6 = 0
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
You could use the quadratic equation right off the bat, or you could factor out a 3 and then use it.
Quadratic equation:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B21x%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=%2821%29%5E2-4%2A12%2A6=153.

Discriminant d=153 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-21%2B-sqrt%28+153+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2821%29%2Bsqrt%28+153+%29%29%2F2%5C12+=+-0.359611796797792
x%5B2%5D+=+%28-%2821%29-sqrt%28+153+%29%29%2F2%5C12+=+-1.39038820320221

Quadratic expression 12x%5E2%2B21x%2B6 can be factored:
12x%5E2%2B21x%2B6+=+12%28x--0.359611796797792%29%2A%28x--1.39038820320221%29
Again, the answer is: -0.359611796797792, -1.39038820320221. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B21%2Ax%2B6+%29