2/9x+1=-2/3x-2

Solution for 2/9x+1=-2/3x-2 equation:

2/9x+1=-2/3x-2

We move all terms to the left:

2/9x+1-(-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+1=0

We calculate fractions


6x/27x^2+18x/27x^2+2+1=0

We add all the numbers together, and all the variables

6x/27x^2+18x/27x^2+3=0

We multiply all the terms by the denominator


6x+18x+3*27x^2=0

We add all the numbers together, and all the variables

24x+3*27x^2=0

Wy multiply elements

81x^2+24x=0

a = 81; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·81·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*81}=\frac{-48}{162}
=-8/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*81}=\frac{0}{162}
=0
$