-2/9x+11/9=1/3x-1

Solution for -2/9x+11/9=1/3x-1 equation:

-2/9x+11/9=1/3x-1

We move all terms to the left:

-2/9x+11/9-(1/3x-1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

-2/9x-1/3x+1+11/9=0

We calculate fractions


(-6x)/2187x^2+(-729x)/2187x^2+33x/2187x^2+1=0

We multiply all the terms by the denominator


(-6x)+(-729x)+33x+1*2187x^2=0

We add all the numbers together, and all the variables

33x+(-6x)+(-729x)+1*2187x^2=0

Wy multiply elements

2187x^2+33x+(-6x)+(-729x)=0

We get rid of parentheses

2187x^2+33x-6x-729x=0

We add all the numbers together, and all the variables

2187x^2-702x=0

a = 2187; b = -702; c = 0;
Δ = b2-4ac
Δ = -7022-4·2187·0
Δ = 492804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{492804}=702$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-702)-702}{2*2187}=\frac{0}{4374}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-702)+702}{2*2187}=\frac{1404}{4374}
=26/81
$