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1/6x+2/3=1/3x-1
We move all terms to the left:
1/6x+2/3-(1/3x-1)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x-1)!=0We get rid of parentheses
x∈R
1/6x-1/3x+1+2/3=0
We calculate fractions
27x/162x^2+(-6x)/162x^2+12x/162x^2+1=0
We multiply all the terms by the denominator
27x+(-6x)+12x+1*162x^2=0
We add all the numbers together, and all the variables
39x+(-6x)+1*162x^2=0
Wy multiply elements
162x^2+39x+(-6x)=0
We get rid of parentheses
162x^2+39x-6x=0
We add all the numbers together, and all the variables
162x^2+33x=0
a = 162; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·162·0
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*162}=\frac{-66}{324} =-11/54 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*162}=\frac{0}{324} =0 $
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