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

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

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

We move all terms to the left:

4/9x+3-(2/3x+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

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

We calculate fractions


12x/27x^2+(-18x)/27x^2-1+3=0

We add all the numbers together, and all the variables

12x/27x^2+(-18x)/27x^2+2=0

We multiply all the terms by the denominator


12x+(-18x)+2*27x^2=0

Wy multiply elements

54x^2+12x+(-18x)=0

We get rid of parentheses

54x^2+12x-18x=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
$