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

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



2/3x-1/2x=1/6
We move all terms to the left:
2/3x-1/2x-(1/6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
2/3x-1/2x-(+1/6)=0
We get rid of parentheses
2/3x-1/2x-1/6=0
We calculate fractions
(-12x^2)/216x^2+144x/216x^2+(-108x)/216x^2=0
We multiply all the terms by the denominator
(-12x^2)+144x+(-108x)=0
We get rid of parentheses
-12x^2+144x-108x=0
We add all the numbers together, and all the variables
-12x^2+36x=0
a = -12; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-12)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-12}=\frac{-72}{-24} =+3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-12}=\frac{0}{-24} =0 $

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