75=0.05r(r+20)

Solution for 75=0.05r(r+20) equation:

75=0.05r(r+20)

We move all terms to the left:

75-(0.05r(r+20))=0


We calculate terms in parentheses: -(0.05r(r+20)), so:

0.05r(r+20)

We multiply parentheses

0r^2+0r

We add all the numbers together, and all the variables

r^2+r

Back to the equation:

-(r^2+r)


We get rid of parentheses

-r^2-r+75=0

We add all the numbers together, and all the variables

-1r^2-1r+75=0

a = -1; b = -1; c = +75;
Δ = b2-4ac
Δ = -12-4·(-1)·75
Δ = 301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{301}}{2*-1}=\frac{1-\sqrt{301}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{301}}{2*-1}=\frac{1+\sqrt{301}}{-2}
$