SOLUTION: solve using quadratic formula {{{3x^2+8x+2=0}}}

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Question 36753: solve using quadratic formula
3x%5E2%2B8x%2B2=0
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2+8x+2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B8x%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=%288%29%5E2-4%2A3%2A2=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+40+%29%29%2F2%5C3+=+-0.279240779943873
x%5B2%5D+=+%28-%288%29-sqrt%28+40+%29%29%2F2%5C3+=+-2.38742588672279

Quadratic expression 3x%5E2%2B8x%2B2 can be factored:
3x%5E2%2B8x%2B2+=+3%28x--0.279240779943873%29%2A%28x--2.38742588672279%29
Again, the answer is: -0.279240779943873, -2.38742588672279. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B8%2Ax%2B2+%29

Hope this helps.
Cheers,
Stan H.