SOLUTION: How do i solve (x+1)/3 = 2/(2x-1) I know it has to be something like: (x+1)(2x-1)=3x2 (x+1)(2x-1)=6 but i don't know how to solve it after that. Thank you!

Algebra ->  Equations -> SOLUTION: How do i solve (x+1)/3 = 2/(2x-1) I know it has to be something like: (x+1)(2x-1)=3x2 (x+1)(2x-1)=6 but i don't know how to solve it after that. Thank you!       Log On


   

Question 750081: How do i solve
(x+1)/3 = 2/(2x-1)
I know it has to be something like:
(x+1)(2x-1)=3x2
(x+1)(2x-1)=6
but i don't know how to solve it after that.
Thank you!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How do i solve
(x+1)/3 = 2/(2x-1)
I know it has to be something like:
(x+1)(2x-1)=3x2 Use * for multiply. x is taken
(x+1)(2x-1)=6
-------
2x^2 + x - 1 = 5
2x^2 + x - 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B1x%2B-6+=+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=%281%29%5E2-4%2A2%2A-6=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+1.5
x%5B2%5D+=+%28-%281%29-sqrt%28+49+%29%29%2F2%5C2+=+-2

Quadratic expression 2x%5E2%2B1x%2B-6 can be factored:
2x%5E2%2B1x%2B-6+=+%28x-1.5%29%2A%28x--2%29
Again, the answer is: 1.5, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B1%2Ax%2B-6+%29