12/2x+4=2/x-2

Solution for 12/2x+4=2/x-2 equation:

12/2x+4=2/x-2

We move all terms to the left:

12/2x+4-(2/x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

12/2x-2/x+2+4=0

We calculate fractions


12x/2x^2+(-4x)/2x^2+2+4=0

We add all the numbers together, and all the variables

12x/2x^2+(-4x)/2x^2+6=0

We multiply all the terms by the denominator


12x+(-4x)+6*2x^2=0

Wy multiply elements

12x^2+12x+(-4x)=0

We get rid of parentheses

12x^2+12x-4x=0

We add all the numbers together, and all the variables

12x^2+8x=0

a = 12; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·12·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*12}=\frac{0}{24}
=0
$