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

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

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

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-18b^2+2b-3b=0

We add all the numbers together, and all the variables

-18b^2-1b=0

a = -18; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-18)·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*-18}=\frac{0}{-36}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-18}=\frac{2}{-36}
=-1/18
$