2/3x-2=6+4/9x

Solution for 2/3x-2=6+4/9x equation:

2/3x-2=6+4/9x

We move all terms to the left:

2/3x-2-(6+4/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(4/9x+6)-2=0

We get rid of parentheses

2/3x-4/9x-6-2=0

We calculate fractions


18x/27x^2+(-12x)/27x^2-6-2=0

We add all the numbers together, and all the variables

18x/27x^2+(-12x)/27x^2-8=0

We multiply all the terms by the denominator


18x+(-12x)-8*27x^2=0

Wy multiply elements

-216x^2+18x+(-12x)=0

We get rid of parentheses

-216x^2+18x-12x=0

We add all the numbers together, and all the variables

-216x^2+6x=0

a = -216; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-216)·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*-216}=\frac{-12}{-432}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-216}=\frac{0}{-432}
=0
$