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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

2/9x-2/3x+2+2/3=0

We calculate fractions


54x/243x^2+(-18x)/243x^2+18x/243x^2+2=0

We multiply all the terms by the denominator


54x+(-18x)+18x+2*243x^2=0

We add all the numbers together, and all the variables

72x+(-18x)+2*243x^2=0

Wy multiply elements

486x^2+72x+(-18x)=0

We get rid of parentheses

486x^2+72x-18x=0

We add all the numbers together, and all the variables

486x^2+54x=0

a = 486; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·486·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*486}=\frac{-108}{972}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*486}=\frac{0}{972}
=0
$