12/2x-1=8/x

Solution for 12/2x-1=8/x equation:

12/2x-1=8/x

We move all terms to the left:

12/2x-1-(8/x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12/2x-(+8/x)-1=0

We get rid of parentheses

12/2x-8/x-1=0

We calculate fractions


12x/2x^2+(-16x)/2x^2-1=0

We multiply all the terms by the denominator


12x+(-16x)-1*2x^2=0

Wy multiply elements

-2x^2+12x+(-16x)=0

We get rid of parentheses

-2x^2+12x-16x=0

We add all the numbers together, and all the variables

-2x^2-4x=0

a = -2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-2)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-2}=\frac{8}{-4}
=-2
$