b/3b+5=8-4b.

Solution for b/3b+5=8-4b. equation:

b/3b+5=8-4b.

We move all terms to the left:

b/3b+5-(8-4b.)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

b/3b-(-4b.+8)+5=0

We get rid of parentheses

b/3b+4b.-8+5=0

We multiply all the terms by the denominator


b+(4b.)*3b-8*3b+5*3b=0

We add all the numbers together, and all the variables

b+(+4b.)*3b-8*3b+5*3b=0

We multiply parentheses

12b^2+b-8*3b+5*3b=0

Wy multiply elements

12b^2+b-24b+15b=0

We add all the numbers together, and all the variables

12b^2-8b=0

a = 12; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·12·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*12}=\frac{0}{24}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*12}=\frac{16}{24}
=2/3
$