R(x)=x(24-x)

Solution for R(x)=x(24-x) equation:

(R)=R(24-R)

We move all terms to the left:

(R)-(R(24-R))=0

We add all the numbers together, and all the variables

R-(R(-1R+24))=0


We calculate terms in parentheses: -(R(-1R+24)), so:

R(-1R+24)

We multiply parentheses

-1R^2+24R

Back to the equation:

-(-1R^2+24R)


We get rid of parentheses

1R^2-24R+R=0

We add all the numbers together, and all the variables

R^2-23R=0

a = 1; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·1·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*1}=\frac{0}{2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*1}=\frac{46}{2}
=23
$