SOLUTION: How do I solve an equation by factoring, if the sum in a fraction? EXAMPLE: 6x + 7 = 20/x

Question 154390: How do I solve an equation by factoring, if the sum in a fraction?
EXAMPLE: 6x + 7 = 20/x
Found 3 solutions by Alan3354, scott8148, ankor@dixie-net.com:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
How do I solve an equation by factoring, if the sum in a fraction?
EXAMPLE: 6x + 7 = 20/x
------------
Multiply thru by x
6x^2 + 7x = 20
6x^2 + 7x - 20 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=529 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.33333333333333, -2.5. Here's your graph:

Once you know the zeros, you can multiply by 2 and 3 to make them integers and figure out how to factor it.
The alternative is trial and error.
(3x-4)*(2x+5)
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
multiplying by x __ 6x^2+7x=20 __ subtracting 20 __ 6x^2+7x-20=0

factoring __(2x+5)(3x-4)=0

2x+5=0 __ x=-5/2

3x-4=0 __ x=4/3
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
6x + 7 = 20/x
;
Multiply both sides by x to get rid of the denominator
x(6x + 7) = 20
:
Mult terms inside the brackets:
6x^2 + 7x = 20
;
Subtract 20 from both sides to reveal our old friend, the quadratic equation
6x^2 + 7x - 20 = 0
:
With diligent effort we can factor this to:
(2x + 5)(3x - 4) = 0
Two solutions
2x = -5
x =
x = -2.5
and
3x = 4
x =
;
:
Check the 1st solution in the original equation
6(-2.5) + 7 =
-15 + 7 = -8
;
Check the 2nd solution
6* + 7 =
8 + 7 = 15
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