5/3b+5=20-b

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

5/3b+5=20-b

We move all terms to the left:

5/3b+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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3b^2-60b+15b+5=0

We add all the numbers together, and all the variables

3b^2-45b+5=0

a = 3; b = -45; c = +5;
Δ = b2-4ac
Δ = -452-4·3·5
Δ = 1965
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{-(-45)-\sqrt{1965}}{2*3}=\frac{45-\sqrt{1965}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1965}}{2*3}=\frac{45+\sqrt{1965}}{6}
$