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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


54x^2/288x^2+48x/288x^2+(-96x)/288x^2=0

We multiply all the terms by the denominator


54x^2+48x+(-96x)=0

We get rid of parentheses

54x^2+48x-96x=0

We add all the numbers together, and all the variables

54x^2-48x=0

a = 54; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·54·0
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*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*54}=\frac{96}{108}
=8/9
$