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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-36x^2)/432x^2+324x/432x^2+(-288x)/432x^2=0

We multiply all the terms by the denominator


(-36x^2)+324x+(-288x)=0

We get rid of parentheses

-36x^2+324x-288x=0

We add all the numbers together, and all the variables

-36x^2+36x=0

a = -36; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-36)·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*-36}=\frac{-72}{-72}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-36}=\frac{0}{-72}
=0
$