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

Solution for -1/3x*2-2/3x+1/9=0 equation:

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


Domain of the equation: 3x*2!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


36x^2/486x^2+(-243x)/486x^2+(-216x)/486x^2=0

We multiply all the terms by the denominator


36x^2+(-243x)+(-216x)=0

We get rid of parentheses

36x^2-243x-216x=0

We add all the numbers together, and all the variables

36x^2-459x=0

a = 36; b = -459; c = 0;
Δ = b2-4ac
Δ = -4592-4·36·0
Δ = 210681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{210681}=459$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-459)-459}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-459)+459}{2*36}=\frac{918}{72}
=12+3/4
$