R(p)=-2.5p^2+650p

Solution for R(p)=-2.5p^2+650p equation:

(R)=-2.5R^2+650R

We move all terms to the left:

(R)-(-2.5R^2+650R)=0

We get rid of parentheses

2.5R^2-650R+R=0

We add all the numbers together, and all the variables

2.5R^2-649R=0

a = 2.5; b = -649; c = 0;
Δ = b2-4ac
Δ = -6492-4·2.5·0
Δ = 421201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{421201}=649$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-649)-649}{2*2.5}=\frac{0}{5}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-649)+649}{2*2.5}=\frac{1298}{5}
=259+3/5
$