5/9x-3/4=2/3x

Solution for 5/9x-3/4=2/3x equation:

5/9x-3/4=2/3x

We move all terms to the left:

5/9x-3/4-(2/3x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=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-(+2/3x)-3/4=0

We get rid of parentheses

5/9x-2/3x-3/4=0

We calculate fractions


(-243x^2)/432x^2+240x/432x^2+(-288x)/432x^2=0

We multiply all the terms by the denominator


(-243x^2)+240x+(-288x)=0

We get rid of parentheses

-243x^2+240x-288x=0

We add all the numbers together, and all the variables

-243x^2-48x=0

a = -243; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-243)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-243}=\frac{0}{-486}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-243}=\frac{96}{-486}
=-16/81
$