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

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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^2-54x=0
a = 32; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·32·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*32}=\frac{0}{64} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*32}=\frac{108}{64} =1+11/16 $

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