R(p)=-0.5p^2+1900p

Solution for R(p)=-0.5p^2+1900p equation:

(R)=-0.5R^2+1900R

We move all terms to the left:

(R)-(-0.5R^2+1900R)=0

We get rid of parentheses

0.5R^2-1900R+R=0

We add all the numbers together, and all the variables

0.5R^2-1899R=0

a = 0.5; b = -1899; c = 0;
Δ = b2-4ac
Δ = -18992-4·0.5·0
Δ = 3606201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3606201}=1899$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1899)-1899}{2*0.5}=\frac{0}{1}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1899)+1899}{2*0.5}=\frac{3798}{1}
=3798
$