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

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



1/3x+1/2-2-x/6x=6
We move all terms to the left:
1/3x+1/2-2-x/6x-(6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
determiningTheFunctionDomain 1/3x-x/6x-2-6+1/2=0
We add all the numbers together, and all the variables
1/3x-x/6x-8+1/2=0
We calculate fractions
(-12x^2)/72x^2+108x^2/72x^2+24x/72x^2-8=0
We multiply all the terms by the denominator
(-12x^2)+108x^2+24x-8*72x^2=0
We add all the numbers together, and all the variables
108x^2+(-12x^2)+24x-8*72x^2=0
Wy multiply elements
108x^2+(-12x^2)-576x^2+24x=0
We get rid of parentheses
108x^2-12x^2-576x^2+24x=0
We add all the numbers together, and all the variables
-480x^2+24x=0
a = -480; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-480)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-480}=\frac{-48}{-960} =1/20 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-480}=\frac{0}{-960} =0 $

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