6/3x=8/2x-2

Solution for 6/3x=8/2x-2 equation:

6/3x=8/2x-2

We move all terms to the left:

6/3x-(8/2x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

6/3x-8/2x+2=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2-12x=0

a = 12; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·12·0
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*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*12}=\frac{24}{24}
=1
$