b=924/b+8

Solution for b=924/b+8 equation:

b=924/b+8

We move all terms to the left:

b-(924/b+8)=0


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

b∈R


We get rid of parentheses

b-924/b-8=0

We multiply all the terms by the denominator


b*b-8*b-924=0

We add all the numbers together, and all the variables

-8b+b*b-924=0

Wy multiply elements

b^2-8b-924=0

a = 1; b = -8; c = -924;
Δ = b2-4ac
Δ = -82-4·1·(-924)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{235}}{2*1}=\frac{8-4\sqrt{235}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{235}}{2*1}=\frac{8+4\sqrt{235}}{2}
$