2/3b=1/6b-4

Solution for 2/3b=1/6b-4 equation:

2/3b=1/6b-4

We move all terms to the left:

2/3b-(1/6b-4)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 6b-4)!=0

b∈R


We get rid of parentheses

2/3b-1/6b+4=0

We calculate fractions


12b/18b^2+(-3b)/18b^2+4=0

We multiply all the terms by the denominator


12b+(-3b)+4*18b^2=0

Wy multiply elements

72b^2+12b+(-3b)=0

We get rid of parentheses

72b^2+12b-3b=0

We add all the numbers together, and all the variables

72b^2+9b=0

a = 72; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·72·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*72}=\frac{-18}{144}
=-1/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*72}=\frac{0}{144}
=0
$