4=12b+8/b+24

Solution for 4=12b+8/b+24 equation:

4=12b+8/b+24

We move all terms to the left:

4-(12b+8/b+24)=0


Domain of the equation: b+24)!=0

b∈R


We get rid of parentheses

-12b-8/b-24+4=0

We multiply all the terms by the denominator


-12b*b-24*b+4*b-8=0

We add all the numbers together, and all the variables

-20b-12b*b-8=0

Wy multiply elements

-12b^2-20b-8=0

a = -12; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·(-12)·(-8)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4}{2*-12}=\frac{16}{-24}
=-2/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4}{2*-12}=\frac{24}{-24}
=-1
$