1/3x-2=4/9x+1

Solution for 1/3x-2=4/9x+1 equation:

1/3x-2=4/9x+1

We move all terms to the left:

1/3x-2-(4/9x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x+1)!=0

x∈R


We get rid of parentheses

1/3x-4/9x-1-2=0

We calculate fractions


9x/27x^2+(-12x)/27x^2-1-2=0

We add all the numbers together, and all the variables

9x/27x^2+(-12x)/27x^2-3=0

We multiply all the terms by the denominator


9x+(-12x)-3*27x^2=0

Wy multiply elements

-81x^2+9x+(-12x)=0

We get rid of parentheses

-81x^2+9x-12x=0

We add all the numbers together, and all the variables

-81x^2-3x=0

a = -81; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-81)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-81}=\frac{0}{-162}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-81}=\frac{6}{-162}
=-1/27
$