SOLUTION: My problem is 5 over 6x minus 8 over 2x = x over 4 I know that you find the common denominator of 12x and multiply everything by it, I come up with the answer 10-48=3x^2; and I

Algebra ->  Rational-functions -> SOLUTION: My problem is 5 over 6x minus 8 over 2x = x over 4 I know that you find the common denominator of 12x and multiply everything by it, I come up with the answer 10-48=3x^2; and I       Log On


   

Question 77022: My problem is 5 over 6x minus 8 over 2x = x over 4
I know that you find the common denominator of 12x and multiply everything by it, I come up with the answer 10-48=3x^2; and I can't get any farther. I know there is more that I need to do, please help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you're trying to solve for x then:
10-48=3x%5E2
-38=3x%5E2 Combine like terms
0=3x%5E2%2B38 Add 38 to both sides
Now use the quadratic formula to solve for x
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B0x%2B38+=+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%2A3%2A38=-456.

The discriminant -456 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -456 is + or - sqrt%28+456%29+=+21.3541565040626.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B0%2Ax%2B38+%29


So this means that there are no real solutions for x. Notice how the graph doesn't intersect with the x-axis.