1/3x+12=7/9x

Solution for 1/3x+12=7/9x equation:

1/3x+12=7/9x

We move all terms to the left:

1/3x+12-(7/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+7/9x)+12=0

We get rid of parentheses

1/3x-7/9x+12=0

We calculate fractions


9x/27x^2+(-21x)/27x^2+12=0

We multiply all the terms by the denominator


9x+(-21x)+12*27x^2=0

Wy multiply elements

324x^2+9x+(-21x)=0

We get rid of parentheses

324x^2+9x-21x=0

We add all the numbers together, and all the variables

324x^2-12x=0

a = 324; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·324·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*324}=\frac{24}{648}
=1/27
$