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

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



1/4x+1/2=1/3x
We move all terms to the left:
1/4x+1/2-(1/3x)=0
Domain of the equation: 4x!=0
x!=0/4
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
1/4x-(+1/3x)+1/2=0
We get rid of parentheses
1/4x-1/3x+1/2=0
We calculate fractions
36x^2/48x^2+12x/48x^2+(-16x)/48x^2=0
We multiply all the terms by the denominator
36x^2+12x+(-16x)=0
We get rid of parentheses
36x^2+12x-16x=0
We add all the numbers together, and all the variables
36x^2-4x=0
a = 36; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·36·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*36}=\frac{0}{72} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*36}=\frac{8}{72} =1/9 $

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