2/3b=6,b

Solution for 2/3b=6,b equation:

2/3b=6.b

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3b-6.b=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

-18b^2+2=0

a = -18; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-18)·2
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{-(0)-12}{2*-18}=\frac{-12}{-36}
=1/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-18}=\frac{12}{-36}
=-1/3
$