SOLUTION: 6xsquared+9x=2

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Question 761426: 6xsquared+9x=2
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean
6%2Ax%5E2+%2B+9%2Ax+=+2 or 6%2Ax%5E2+%2B+9%2Ax+-+2+=+0
This is a standard quadratic equation which can be solved using the quadratic solver, as shown below.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B9x%2B-2+=+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=%289%29%5E2-4%2A6%2A-2=129.

Discriminant d=129 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+129+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+129+%29%29%2F2%5C6+=+0.196484724300046
x%5B2%5D+=+%28-%289%29-sqrt%28+129+%29%29%2F2%5C6+=+-1.69648472430005

Quadratic expression 6x%5E2%2B9x%2B-2 can be factored:
6x%5E2%2B9x%2B-2+=+6%28x-0.196484724300046%29%2A%28x--1.69648472430005%29
Again, the answer is: 0.196484724300046, -1.69648472430005. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B9%2Ax%2B-2+%29