1/b=12/3b+4

Solution for 1/b=12/3b+4 equation:

1/b=12/3b+4

We move all terms to the left:

1/b-(12/3b+4)=0


Domain of the equation: b!=0

b∈R



Domain of the equation: 3b+4)!=0

b∈R


We get rid of parentheses

1/b-12/3b-4=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12b^2-9b=0

a = -12; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-12)·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*-12}=\frac{0}{-24}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-12}=\frac{18}{-24}
=-3/4
$