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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


18x/27x^2+18x/27x^2+2+4=0

We add all the numbers together, and all the variables

18x/27x^2+18x/27x^2+6=0

We multiply all the terms by the denominator


18x+18x+6*27x^2=0

We add all the numbers together, and all the variables

36x+6*27x^2=0

Wy multiply elements

162x^2+36x=0

a = 162; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·162·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*162}=\frac{-72}{324}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*162}=\frac{0}{324}
=0
$