SOLUTION: Solve using quadratic formula show all work 3n^2+12n=-5

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Question 1094598: Solve using quadratic formula show all work
3n^2+12n=-5
Found 2 solutions by addingup, Alan3354:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
3n^2+12n = -5
3n^2+12n+5 = 0
n = (-12+sqrt(12^2-4*3*5))/2*3
n = (-12+sqrt(144-60))/6
n = (-12+sqrt84)/6
n = (9.165-12)/6
n = -0.4725

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3n^2+12n=-5
3n^2 + 12n + 5 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B12x%2B5+=+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=%2812%29%5E2-4%2A3%2A5=84.

Discriminant d=84 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+84+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+84+%29%29%2F2%5C3+=+-0.472474768348053
x%5B2%5D+=+%28-%2812%29-sqrt%28+84+%29%29%2F2%5C3+=+-3.52752523165195

Quadratic expression 3x%5E2%2B12x%2B5 can be factored:
3x%5E2%2B12x%2B5+=+%28x--0.472474768348053%29%2A%28x--3.52752523165195%29
Again, the answer is: -0.472474768348053, -3.52752523165195. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B12%2Ax%2B5+%29

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Ignore the statement that it can be factored.
It can't.