R(p)=-5p^2+15000p

Solution for R(p)=-5p^2+15000p equation:

(R)=-5R^2+15000R

We move all terms to the left:

(R)-(-5R^2+15000R)=0

We get rid of parentheses

5R^2-15000R+R=0

We add all the numbers together, and all the variables

5R^2-14999R=0

a = 5; b = -14999; c = 0;
Δ = b2-4ac
Δ = -149992-4·5·0
Δ = 224970001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{224970001}=14999$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14999)-14999}{2*5}=\frac{0}{10}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14999)+14999}{2*5}=\frac{29998}{10}
=2999+4/5
$