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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


32x^2/72x^2+36x/72x^2+(-18x)/72x^2=0

We multiply all the terms by the denominator


32x^2+36x+(-18x)=0

We get rid of parentheses

32x^2+36x-18x=0

We add all the numbers together, and all the variables

32x^2+18x=0

a = 32; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·32·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*32}=\frac{-36}{64}
=-9/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*32}=\frac{0}{64}
=0
$