3/5b+5=20-b

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

3/5b+5=20-b

We move all terms to the left:

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


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5b^2-100b+25b+3=0

We add all the numbers together, and all the variables

5b^2-75b+3=0

a = 5; b = -75; c = +3;
Δ = b2-4ac
Δ = -752-4·5·3
Δ = 5565
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{-(-75)-\sqrt{5565}}{2*5}=\frac{75-\sqrt{5565}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5565}}{2*5}=\frac{75+\sqrt{5565}}{10}
$