3-2/9b=1/6b-7

Solution for 3-2/9b=1/6b-7 equation:

3-2/9b=1/6b-7

We move all terms to the left:

3-2/9b-(1/6b-7)=0


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R



Domain of the equation: 6b-7)!=0

b∈R


We get rid of parentheses

-2/9b-1/6b+7+3=0

We calculate fractions


(-12b)/54b^2+(-9b)/54b^2+7+3=0

We add all the numbers together, and all the variables

(-12b)/54b^2+(-9b)/54b^2+10=0

We multiply all the terms by the denominator


(-12b)+(-9b)+10*54b^2=0

Wy multiply elements

540b^2+(-12b)+(-9b)=0

We get rid of parentheses

540b^2-12b-9b=0

We add all the numbers together, and all the variables

540b^2-21b=0

a = 540; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·540·0
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*540}=\frac{0}{1080}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*540}=\frac{42}{1080}
=7/180
$