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

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



1/2-2/3x=5/6x-2
We move all terms to the left:
1/2-2/3x-(5/6x-2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x-2)!=0
x∈R
We get rid of parentheses
-2/3x-5/6x+2+1/2=0
We calculate fractions
108x^2/72x^2+(-48x)/72x^2+(-60x)/72x^2+2=0
We multiply all the terms by the denominator
108x^2+(-48x)+(-60x)+2*72x^2=0
Wy multiply elements
108x^2+144x^2+(-48x)+(-60x)=0
We get rid of parentheses
108x^2+144x^2-48x-60x=0
We add all the numbers together, and all the variables
252x^2-108x=0
a = 252; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·252·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*252}=\frac{0}{504} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*252}=\frac{216}{504} =3/7 $

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