3-2/9b=1/6b-1

Solution for 3-2/9b=1/6b-1 equation:

3-2/9b=1/6b-1

We move all terms to the left:

3-2/9b-(1/6b-1)=0


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R



Domain of the equation: 6b-1)!=0

b∈R


We get rid of parentheses

-2/9b-1/6b+1+3=0

We calculate fractions


(-12b)/54b^2+(-9b)/54b^2+1+3=0

We add all the numbers together, and all the variables

(-12b)/54b^2+(-9b)/54b^2+4=0

We multiply all the terms by the denominator


(-12b)+(-9b)+4*54b^2=0

Wy multiply elements

216b^2+(-12b)+(-9b)=0

We get rid of parentheses

216b^2-12b-9b=0

We add all the numbers together, and all the variables

216b^2-21b=0

a = 216; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·216·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*216}=\frac{0}{432}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*216}=\frac{42}{432}
=7/72
$