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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/432x^2+288x/432x^2+(-324x)/432x^2-1=0

We multiply all the terms by the denominator


48x^2+288x+(-324x)-1*432x^2=0

Wy multiply elements

48x^2-432x^2+288x+(-324x)=0

We get rid of parentheses

48x^2-432x^2+288x-324x=0

We add all the numbers together, and all the variables

-384x^2-36x=0

a = -384; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-384)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-384}=\frac{0}{-768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-384}=\frac{72}{-768}
=-3/32
$