2/3b=8-2b

Solution for 2/3b=8-2b equation:

2/3b=8-2b

We move all terms to the left:

2/3b-(8-2b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

2/3b-(-2b+8)=0

We get rid of parentheses

2/3b+2b-8=0

We multiply all the terms by the denominator


2b*3b-8*3b+2=0

Wy multiply elements

6b^2-24b+2=0

a = 6; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·6·2
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{33}}{2*6}=\frac{24-4\sqrt{33}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{33}}{2*6}=\frac{24+4\sqrt{33}}{12}
$