2/6x=4/9x-1

Solution for 2/6x=4/9x-1 equation:

2/6x=4/9x-1

We move all terms to the left:

2/6x-(4/9x-1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/6x-4/9x+1=0

We calculate fractions


18x/54x^2+(-24x)/54x^2+1=0

We multiply all the terms by the denominator


18x+(-24x)+1*54x^2=0

Wy multiply elements

54x^2+18x+(-24x)=0

We get rid of parentheses

54x^2+18x-24x=0

We add all the numbers together, and all the variables

54x^2-6x=0

a = 54; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·54·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*54}=\frac{12}{108}
=1/9
$