R=2.5p^2+500p

Solution for R=2.5p^2+500p equation:

=2.5R^2+500R

We move all terms to the left:

-(2.5R^2+500R)=0

We get rid of parentheses

-2.5R^2-500R=0

a = -2.5; b = -500; c = 0;
Δ = b2-4ac
Δ = -5002-4·(-2.5)·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-500}{2*-2.5}=\frac{0}{-5}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+500}{2*-2.5}=\frac{1000}{-5}
=-200
$