12/3x+2=8/x-4

Solution for 12/3x+2=8/x-4 equation:

12/3x+2=8/x-4

We move all terms to the left:

12/3x+2-(8/x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

12/3x-8/x+4+2=0

We calculate fractions


12x/3x^2+(-24x)/3x^2+4+2=0

We add all the numbers together, and all the variables

12x/3x^2+(-24x)/3x^2+6=0

We multiply all the terms by the denominator


12x+(-24x)+6*3x^2=0

Wy multiply elements

18x^2+12x+(-24x)=0

We get rid of parentheses

18x^2+12x-24x=0

We add all the numbers together, and all the variables

18x^2-12x=0

a = 18; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·18·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*18}=\frac{24}{36}
=2/3
$