SOLUTION: I have the problem almost complete but I can get this, Here is the problem: 2/x - 1 = -6 5/x - 2 I got this far an I get stock {{{6x^2-21x+13=0}}} ( ? )( ?

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Question 211730: I have the problem almost complete but I can get this, Here is the problem:
2/x - 1 = -6 5/x - 2
I got this far an I get stock
6x%5E2-21x%2B13=0
( ? )( ? )
I can get two #'s to solve this equation? Maybe it can be solve... I need some help...
Answer by gypsy1274(9) About Me  (Show Source):
You can put this solution on YOUR website!
First, I must point out that your two equations are not equal. Unless I am misunderstanding the original equation, you have given 2 different problems.
For the first equation, I understand it to read like this:
2%2Fx-1=%28-6%295%2Fx-2
Start by multiplying the entire equation by x to eliminate the fraction.
2-x=-30-2x
To solve for x, move all the x terms to the left side of the equation and all the non x terms to the right side.
Add 2x to each side to move the -2x to the left. Remember that what you do to one side of the equation, you have to do to the other.
2-x%2B2x=-30-2x%2B2x
Combine like terms to get:
2%2Bx=-30
Now move all non x terms to the right side by subtracting 2 from both sides.
-2%2B2%2Bx=-30-2
Combine like terms again and the result is:
x=-32

For your second equation, you must use the quadratic equation to solve this problem.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
You've already got the equation in to ax%5E2%2Bbx%2Bc form, so just plug in the numbers.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-21x%2B13+=+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=%28-21%29%5E2-4%2A6%2A13=129.

Discriminant d=129 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+129+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+129+%29%29%2F2%5C6+=+2.69648472430005
x%5B2%5D+=+%28-%28-21%29-sqrt%28+129+%29%29%2F2%5C6+=+0.803515275699954

Quadratic expression 6x%5E2%2B-21x%2B13 can be factored:
6x%5E2%2B-21x%2B13+=+6%28x-2.69648472430005%29%2A%28x-0.803515275699954%29
Again, the answer is: 2.69648472430005, 0.803515275699954. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-21%2Ax%2B13+%29



If this doesn't answer your question, feel free to contact me at http://www.ziizoo.com/profile/gypsy1274 for a free 30 minute tutor session.