3b=-1/3b-8

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

3b=-1/3b-8

We move all terms to the left:

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


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

b∈R


We get rid of parentheses

3b+1/3b+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

9b^2+24b+1=0

a = 9; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·9·1
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{15}}{2*9}=\frac{-24-6\sqrt{15}}{18}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{15}}{2*9}=\frac{-24+6\sqrt{15}}{18}
$