SOLUTION: use the quadratic formula to solve the following quadratic equations. a. 3x^2+2x-8=0 b. 5x^2+7x=12 please help

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Question 6687: use the quadratic formula to solve the following quadratic equations.
a. 3x^2+2x-8=0
b. 5x^2+7x=12

please help
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do one and you do another, okay?
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B2x%2B-8+=+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=%282%29%5E2-4%2A3%2A-8=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C3+=+1.33333333333333
x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C3+=+-2

Quadratic expression 3x%5E2%2B2x%2B-8 can be factored:
3x%5E2%2B2x%2B-8+=+3%28x-1.33333333333333%29%2A%28x--2%29
Again, the answer is: 1.33333333333333, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-8+%29