SOLUTION: 3x^2+6x+1=0

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Question 943520: 3x^2+6x+1=0
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B6x%2B1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B6x%2B1+=+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=%286%29%5E2-4%2A3%2A1=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+24+%29%29%2F2%5C3+=+-0.183503419072274
x%5B2%5D+=+%28-%286%29-sqrt%28+24+%29%29%2F2%5C3+=+-1.81649658092773

Quadratic expression 3x%5E2%2B6x%2B1 can be factored:
3x%5E2%2B6x%2B1+=+3%28x--0.183503419072274%29%2A%28x--1.81649658092773%29
Again, the answer is: -0.183503419072274, -1.81649658092773. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B6%2Ax%2B1+%29