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5/6x-2=2/3x+1
We move all terms to the left:
5/6x-2-(2/3x+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
5/6x-2/3x-1-2=0
We calculate fractions
15x/18x^2+(-12x)/18x^2-1-2=0
We add all the numbers together, and all the variables
15x/18x^2+(-12x)/18x^2-3=0
We multiply all the terms by the denominator
15x+(-12x)-3*18x^2=0
Wy multiply elements
-54x^2+15x+(-12x)=0
We get rid of parentheses
-54x^2+15x-12x=0
We add all the numbers together, and all the variables
-54x^2+3x=0
a = -54; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-54)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-54}=\frac{-6}{-108} =1/18 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-54}=\frac{0}{-108} =0 $
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