2/3b+3=20-b

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

2/3b+3=20-b

We move all terms to the left:

2/3b+3-(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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3b^2-60b+9b+2=0

We add all the numbers together, and all the variables

3b^2-51b+2=0

a = 3; b = -51; c = +2;
Δ = b2-4ac
Δ = -512-4·3·2
Δ = 2577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2577}}{2*3}=\frac{51-\sqrt{2577}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2577}}{2*3}=\frac{51+\sqrt{2577}}{6}
$