5/6x-2=1-2/3x

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Solution for 5/6x-2=1-2/3x equation:



5/6x-2=1-2/3x
We move all terms to the left:
5/6x-2-(1-2/3x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
5/6x-(-2/3x+1)-2=0
We get rid of parentheses
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
We add all the numbers together, and all the variables
27x-3*18x^2=0
Wy multiply elements
-54x^2+27x=0
a = -54; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-54)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-54}=\frac{-54}{-108} =1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-54}=\frac{0}{-108} =0 $

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