SOLUTION: what are the solution of this equation 2x + 5/2 = 3/x

Algebra ->  Radicals -> SOLUTION: what are the solution of this equation 2x + 5/2 = 3/x      Log On


   

Question 971038: what are the solution of this equation 2x + 5/2 = 3/x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
what are the solution of this equation 2x + 5/2 = 3/x
------------
2x+%2B+5%2F2+=+3%2Fx
Multiply thru by 2x
4x%5E2+%2B+5x+=+6
4x%5E2+%2B+5x+-+6+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B5x%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=%285%29%5E2-4%2A4%2A-6=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+121+%29%29%2F2%5C4+=+0.75
x%5B2%5D+=+%28-%285%29-sqrt%28+121+%29%29%2F2%5C4+=+-2

Quadratic expression 4x%5E2%2B5x%2B-6 can be factored:
4x%5E2%2B5x%2B-6+=+%28x-0.75%29%2A%28x--2%29
Again, the answer is: 0.75, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B5%2Ax%2B-6+%29

---
x = 3/4, x = -2