3/3x-6=4/2x+4

Solution for 3/3x-6=4/2x+4 equation:

3/3x-6=4/2x+4

We move all terms to the left:

3/3x-6-(4/2x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

3/3x-4/2x-4-6=0

We calculate fractions


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

We add all the numbers together, and all the variables

6x/6x^2+(-12x)/6x^2-10=0

We multiply all the terms by the denominator


6x+(-12x)-10*6x^2=0

Wy multiply elements

-60x^2+6x+(-12x)=0

We get rid of parentheses

-60x^2+6x-12x=0

We add all the numbers together, and all the variables

-60x^2-6x=0

a = -60; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-60)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-60}=\frac{12}{-120}
=-1/10
$