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5/6x-3=1/3x
We move all terms to the left:
5/6x-3-(1/3x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/6x-(+1/3x)-3=0
We get rid of parentheses
5/6x-1/3x-3=0
We calculate fractions
15x/18x^2+(-6x)/18x^2-3=0
We multiply all the terms by the denominator
15x+(-6x)-3*18x^2=0
Wy multiply elements
-54x^2+15x+(-6x)=0
We get rid of parentheses
-54x^2+15x-6x=0
We add all the numbers together, and all the variables
-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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