SOLUTION: 3/4x^2+8x+20=0

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Question 902888: 3/4x^2+8x+20=0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
3/4x^2+8x+20=0 Multiplying thru by 4 so as all denominators = 1
3x^2 + 32x + 80 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B32x%2B80+=+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=%2832%29%5E2-4%2A3%2A80=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+64+%29%29%2F2%5C3+=+-4
x%5B2%5D+=+%28-%2832%29-sqrt%28+64+%29%29%2F2%5C3+=+-6.66666666666667

Quadratic expression 3x%5E2%2B32x%2B80 can be factored:
3x%5E2%2B32x%2B80+=+3%28x--4%29%2A%28x--6.66666666666667%29
Again, the answer is: -4, -6.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B32%2Ax%2B80+%29