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2/3x-2=1/6x
We move all terms to the left:
2/3x-2-(1/6x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(+1/6x)-2=0
We get rid of parentheses
2/3x-1/6x-2=0
We calculate fractions
12x/18x^2+(-3x)/18x^2-2=0
We multiply all the terms by the denominator
12x+(-3x)-2*18x^2=0
Wy multiply elements
-36x^2+12x+(-3x)=0
We get rid of parentheses
-36x^2+12x-3x=0
We add all the numbers together, and all the variables
-36x^2+9x=0
a = -36; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-36)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-36}=\frac{-18}{-72} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-36}=\frac{0}{-72} =0 $
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