b=5/3b+8

Solution for b=5/3b+8 equation:

b=5/3b+8

We move all terms to the left:

b-(5/3b+8)=0


Domain of the equation: 3b+8)!=0

b∈R


We get rid of parentheses

b-5/3b-8=0

We multiply all the terms by the denominator


b*3b-8*3b-5=0

Wy multiply elements

3b^2-24b-5=0

a = 3; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·3·(-5)
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{159}}{2*3}=\frac{24-2\sqrt{159}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{159}}{2*3}=\frac{24+2\sqrt{159}}{6}
$