(5/9x+12)=2/3x

Solution for (5/9x+12)=2/3x equation:

(5/9x+12)=2/3x

We move all terms to the left:

(5/9x+12)-(2/3x)=0


Domain of the equation: 9x+12)!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(5/9x+12)-(+2/3x)=0

We get rid of parentheses

5/9x-2/3x+12=0

We calculate fractions


15x/27x^2+(-18x)/27x^2+12=0

We multiply all the terms by the denominator


15x+(-18x)+12*27x^2=0

Wy multiply elements

324x^2+15x+(-18x)=0

We get rid of parentheses

324x^2+15x-18x=0

We add all the numbers together, and all the variables

324x^2-3x=0

a = 324; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·324·0
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*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*324}=\frac{6}{648}
=1/108
$