(9/12b)+9=b

Solution for (9/12b)+9=b equation:

(9/12b)+9=b

We move all terms to the left:

(9/12b)+9-(b)=0


Domain of the equation: 12b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

(+9/12b)-b+9=0

We add all the numbers together, and all the variables

-1b+(+9/12b)+9=0

We get rid of parentheses

-1b+9/12b+9=0

We multiply all the terms by the denominator


-1b*12b+9*12b+9=0

Wy multiply elements

-12b^2+108b+9=0

a = -12; b = 108; c = +9;
Δ = b2-4ac
Δ = 1082-4·(-12)·9
Δ = 12096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-24\sqrt{21}}{2*-12}=\frac{-108-24\sqrt{21}}{-24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+24\sqrt{21}}{2*-12}=\frac{-108+24\sqrt{21}}{-24}
$