R(x)=x(20-0.06x)

Solution for R(x)=x(20-0.06x) equation:

(R)=R(20-0.06R)

We move all terms to the left:

(R)-(R(20-0.06R))=0

We add all the numbers together, and all the variables

R-(R(-0.06R+20))=0


We calculate terms in parentheses: -(R(-0.06R+20)), so:

R(-0.06R+20)

We multiply parentheses

0R^2+20R

We add all the numbers together, and all the variables

R^2+20R

Back to the equation:

-(R^2+20R)


We get rid of parentheses

-R^2+R-20R=0

We add all the numbers together, and all the variables

-1R^2-19R=0

a = -1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-1)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-1}=\frac{0}{-2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-1}=\frac{38}{-2}
=-19
$