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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/27x^2+(-9x)/27x^2+4-3=0

We add all the numbers together, and all the variables

6x/27x^2+(-9x)/27x^2+1=0

We multiply all the terms by the denominator


6x+(-9x)+1*27x^2=0

Wy multiply elements

27x^2+6x+(-9x)=0

We get rid of parentheses

27x^2+6x-9x=0

We add all the numbers together, and all the variables

27x^2-3x=0

a = 27; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·27·0
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*27}=\frac{0}{54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*27}=\frac{6}{54}
=1/9
$