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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

54x^2+3x+(-9x)=0

We get rid of parentheses

54x^2+3x-9x=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
$