1/3x+2=5-1/6x

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Solution for 1/3x+2=5-1/6x equation:



1/3x+2=5-1/6x
We move all terms to the left:
1/3x+2-(5-1/6x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/3x-(-1/6x+5)+2=0
We get rid of parentheses
1/3x+1/6x-5+2=0
We calculate fractions
6x/18x^2+3x/18x^2-5+2=0
We add all the numbers together, and all the variables
6x/18x^2+3x/18x^2-3=0
We multiply all the terms by the denominator
6x+3x-3*18x^2=0
We add all the numbers together, and all the variables
9x-3*18x^2=0
Wy multiply elements
-54x^2+9x=0
a = -54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-54)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-54}=\frac{-18}{-108} =1/6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-54}=\frac{0}{-108} =0 $

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