SOLUTION: Professor I'm suppose to use the quadratic formula to solve but my answer is not matching my choices. The problem is 3nČ=-6n-1 I moved everything to one side and I got -6-+2&#8

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Question 647349: Professor I'm suppose to use the quadratic formula to solve but my answer is not matching my choices.
The problem is 3nČ=-6n-1
I moved everything to one side and I got -6-+2√6/6 but its not one of my options. Need your help thanks!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is 3nČ=-6n-1
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3n%5E2+%2B+6x+%2B+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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+=+%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

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n = -1 ± sqrt(6)/3
Maybe you didn't reduce it.