SOLUTION: 6x^2 + 10x = -2

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Question 143962: 6x^2 + 10x = -2
Answer by nabla(475) About Me  (Show Source):
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6x^2 + 10x = -2
6x^2 + 10x +2= 0
3x^2+5x+1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B5x%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=%285%29%5E2-4%2A3%2A1=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+-0.232408120756002
x%5B2%5D+=+%28-%285%29-sqrt%28+13+%29%29%2F2%5C3+=+-1.43425854591066

Quadratic expression 3x%5E2%2B5x%2B1 can be factored:
3x%5E2%2B5x%2B1+=+3%28x--0.232408120756002%29%2A%28x--1.43425854591066%29
Again, the answer is: -0.232408120756002, -1.43425854591066. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B5%2Ax%2B1+%29