1/6x+12=1/3x+10

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Solution for 1/6x+12=1/3x+10 equation:



1/6x+12=1/3x+10
We move all terms to the left:
1/6x+12-(1/3x+10)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x+10)!=0
x∈R
We get rid of parentheses
1/6x-1/3x-10+12=0
We calculate fractions
3x/18x^2+(-6x)/18x^2-10+12=0
We add all the numbers together, and all the variables
3x/18x^2+(-6x)/18x^2+2=0
We multiply all the terms by the denominator
3x+(-6x)+2*18x^2=0
Wy multiply elements
36x^2+3x+(-6x)=0
We get rid of parentheses
36x^2+3x-6x=0
We add all the numbers together, and all the variables
36x^2-3x=0
a = 36; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·36·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*36}=\frac{0}{72} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*36}=\frac{6}{72} =1/12 $

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