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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-48x^2)/432x^2+288x/432x^2+(-540x)/432x^2=0

We multiply all the terms by the denominator


(-48x^2)+288x+(-540x)=0

We get rid of parentheses

-48x^2+288x-540x=0

We add all the numbers together, and all the variables

-48x^2-252x=0

a = -48; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·(-48)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*-48}=\frac{504}{-96}
=-5+1/4
$