2/3x-3/4=5/6x+1

Solution for 2/3x-3/4=5/6x+1 equation:

2/3x-3/4=5/6x+1

We move all terms to the left:

2/3x-3/4-(5/6x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

2/3x-5/6x-1-3/4=0

We calculate fractions


(-324x^2)/288x^2+192x/288x^2+(-240x)/288x^2-1=0

We multiply all the terms by the denominator


(-324x^2)+192x+(-240x)-1*288x^2=0

Wy multiply elements

(-324x^2)-288x^2+192x+(-240x)=0

We get rid of parentheses

-324x^2-288x^2+192x-240x=0

We add all the numbers together, and all the variables

-612x^2-48x=0

a = -612; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-612)·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*-612}=\frac{0}{-1224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-612}=\frac{96}{-1224}
=-4/51
$