R(p)=-6p^2+18000

Solution for R(p)=-6p^2+18000 equation:

(R)=-6R^2+18000

We move all terms to the left:

(R)-(-6R^2+18000)=0

We get rid of parentheses

6R^2+R-18000=0

a = 6; b = 1; c = -18000;
Δ = b2-4ac
Δ = 12-4·6·(-18000)
Δ = 432001
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{432001}}{2*6}=\frac{-1-\sqrt{432001}}{12}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{432001}}{2*6}=\frac{-1+\sqrt{432001}}{12}
$