1/2-1/6b=2/3b

Solution for 1/2-1/6b=2/3b equation:

1/2-1/6b=2/3b

We move all terms to the left:

1/2-1/6b-(2/3b)=0


Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R



Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-1/6b-(+2/3b)+1/2=0

We get rid of parentheses

-1/6b-2/3b+1/2=0

We calculate fractions


54b^2/72b^2+(-12b)/72b^2+(-48b)/72b^2=0

We multiply all the terms by the denominator


54b^2+(-12b)+(-48b)=0

We get rid of parentheses

54b^2-12b-48b=0

We add all the numbers together, and all the variables

54b^2-60b=0

a = 54; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·54·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*54}=\frac{0}{108}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*54}=\frac{120}{108}
=1+1/9
$