2/3x-5/4=5/6x

Solution for 2/3x-5/4=5/6x equation:

2/3x-5/4=5/6x

We move all terms to the left:

2/3x-5/4-(5/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(+5/6x)-5/4=0

We get rid of parentheses

2/3x-5/6x-5/4=0

We calculate fractions


(-540x^2)/288x^2+192x/288x^2+(-240x)/288x^2=0

We multiply all the terms by the denominator


(-540x^2)+192x+(-240x)=0

We get rid of parentheses

-540x^2+192x-240x=0

We add all the numbers together, and all the variables

-540x^2-48x=0

a = -540; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-540)·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*-540}=\frac{0}{-1080}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-540}=\frac{96}{-1080}
=-4/45
$