2b/3b+5=20-b

Solution for 2b/3b+5=20-b equation:

2b/3b+5=20-b

We move all terms to the left:

2b/3b+5-(20-b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

2b/3b-(-1b+20)+5=0

We get rid of parentheses

2b/3b+1b-20+5=0

We multiply all the terms by the denominator


2b+1b*3b-20*3b+5*3b=0

Wy multiply elements

3b^2+2b-60b+15b=0

We add all the numbers together, and all the variables

3b^2-43b=0

a = 3; b = -43; c = 0;
Δ = b2-4ac
Δ = -432-4·3·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-43}{2*3}=\frac{0}{6}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+43}{2*3}=\frac{86}{6}
=14+1/3
$