R=0.5p^2+1900p

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

=0.5R^2+1900R

We move all terms to the left:

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

We get rid of parentheses

-0.5R^2-1900R=0

a = -0.5; b = -1900; c = 0;
Δ = b2-4ac
Δ = -19002-4·(-0.5)·0
Δ = 3610000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3610000}=1900$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1900)-1900}{2*-0.5}=\frac{0}{-1}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1900)+1900}{2*-0.5}=\frac{3800}{-1}
=-3800
$