SOLUTION: How would you solve the following equation by using the quadratic formula? {{{3/4x^2=1/2x+1/3}}} Thanks!

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Question 168794: How would you solve the following equation by using the quadratic formula?

3%2F4x%5E2=1%2F2x%2B1%2F3

Thanks!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F4x%5E2=1%2F2x%2B1%2F3
Multiply both sides by 12x^2 to get:
9=6x%2B4x%5E2
9=4x%5E2%2B6x
0=4x%5E2%2B6x-9
Now, you can apply your quadratic equation to get the solution of:
x ={0.927, -2.427}
.
Details below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B6x%2B-9+=+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=%286%29%5E2-4%2A4%2A-9=180.

Discriminant d=180 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+180+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+180+%29%29%2F2%5C4+=+0.927050983124842
x%5B2%5D+=+%28-%286%29-sqrt%28+180+%29%29%2F2%5C4+=+-2.42705098312484

Quadratic expression 4x%5E2%2B6x%2B-9 can be factored:
4x%5E2%2B6x%2B-9+=+4%28x-0.927050983124842%29%2A%28x--2.42705098312484%29
Again, the answer is: 0.927050983124842, -2.42705098312484. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B6%2Ax%2B-9+%29