4=b+24/12b+8

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

4=b+24/12b+8

We move all terms to the left:

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


Domain of the equation: 12b+8)!=0

b∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12b^2-96b+48b-24=0

We add all the numbers together, and all the variables

-12b^2-48b-24=0

a = -12; b = -48; c = -24;
Δ = b2-4ac
Δ = -482-4·(-12)·(-24)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{2}}{2*-12}=\frac{48-24\sqrt{2}}{-24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{2}}{2*-12}=\frac{48+24\sqrt{2}}{-24}
$