R(p)=-6p^2+24,000

Solution for R(p)=-6p^2+24,000 equation:

(R)=-6R^2+24.000

We move all terms to the left:

(R)-(-6R^2+24.000)=0

We get rid of parentheses

6R^2+R-24.000=0

We add all the numbers together, and all the variables

6R^2+R-24=0

a = 6; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·6·(-24)
Δ = 577
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{577}}{2*6}=\frac{-1-\sqrt{577}}{12}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{577}}{2*6}=\frac{-1+\sqrt{577}}{12}
$