1/2b+6=1/3b

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

1/2b+6=1/3b

We move all terms to the left:

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


Domain of the equation: 2b!=0

b!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

36b^2+3b+(-2b)=0

We get rid of parentheses

36b^2+3b-2b=0

We add all the numbers together, and all the variables

36b^2+b=0

a = 36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·36·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*36}=\frac{-2}{72}
=-1/36
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*36}=\frac{0}{72}
=0
$