R(x)=48000x-6x^2

Solution for R(x)=48000x-6x^2 equation:

(R)=48000R-6R^2

We move all terms to the left:

(R)-(48000R-6R^2)=0

We get rid of parentheses

6R^2-48000R+R=0

We add all the numbers together, and all the variables

6R^2-47999R=0

a = 6; b = -47999; c = 0;
Δ = b2-4ac
Δ = -479992-4·6·0
Δ = 2303904001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2303904001}=47999$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47999)-47999}{2*6}=\frac{0}{12}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47999)+47999}{2*6}=\frac{95998}{12}
=7999+5/6
$