SOLUTION: Could you please help me to understand the process of solving for x: x^2-7=2-5x^2

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Question 801720: Could you please help me to understand the process of solving for x:
x^2-7=2-5x^2
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-7=2-5x^2
x^2+5x^2-2-7=0
6x^2-9=0
2x^2-3=0
x= sqrt(6)/2, x= -sqrt(6)/2 see below
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B0x%2B-3+=+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=%280%29%5E2-4%2A2%2A-3=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+24+%29%29%2F2%5C2+=+1.22474487139159
x%5B2%5D+=+%28-%280%29-sqrt%28+24+%29%29%2F2%5C2+=+-1.22474487139159

Quadratic expression 2x%5E2%2B0x%2B-3 can be factored:
2x%5E2%2B0x%2B-3+=+2%28x-1.22474487139159%29%2A%28x--1.22474487139159%29
Again, the answer is: 1.22474487139159, -1.22474487139159. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B0%2Ax%2B-3+%29