8+b=1/3b

Solution for 8+b=1/3b equation:

8+b=1/3b

We move all terms to the left:

8+b-(1/3b)=0


Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

b-(+1/3b)+8=0

We get rid of parentheses

b-1/3b+8=0

We multiply all the terms by the denominator


b*3b+8*3b-1=0

Wy multiply elements

3b^2+24b-1=0

a = 3; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·3·(-1)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-14\sqrt{3}}{2*3}=\frac{-24-14\sqrt{3}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+14\sqrt{3}}{2*3}=\frac{-24+14\sqrt{3}}{6}
$