3-2/6b=1/3b

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

3-2/6b=1/3b

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


(-6b)/18b^2+(-6b)/18b^2+3=0

We multiply all the terms by the denominator


(-6b)+(-6b)+3*18b^2=0

Wy multiply elements

54b^2+(-6b)+(-6b)=0

We get rid of parentheses

54b^2-6b-6b=0

We add all the numbers together, and all the variables

54b^2-12b=0

a = 54; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·54·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*54}=\frac{0}{108}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*54}=\frac{24}{108}
=2/9
$