R(x)=x(60-3x)

Solution for R(x)=x(60-3x) equation:

(R)=R(60-3R)

We move all terms to the left:

(R)-(R(60-3R))=0

We add all the numbers together, and all the variables

R-(R(-3R+60))=0


We calculate terms in parentheses: -(R(-3R+60)), so:

R(-3R+60)

We multiply parentheses

-3R^2+60R

Back to the equation:

-(-3R^2+60R)


We get rid of parentheses

3R^2-60R+R=0

We add all the numbers together, and all the variables

3R^2-59R=0

a = 3; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·3·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*3}=\frac{0}{6}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*3}=\frac{118}{6}
=19+2/3
$