R(p)=p(-2.5p+800)

Solution for R(p)=p(-2.5p+800) equation:

(R)=R(-2.5R+800)

We move all terms to the left:

(R)-(R(-2.5R+800))=0


We calculate terms in parentheses: -(R(-2.5R+800)), so:

R(-2.5R+800)

We multiply parentheses

-2R^2+800R

Back to the equation:

-(-2R^2+800R)


We get rid of parentheses

2R^2-800R+R=0

We add all the numbers together, and all the variables

2R^2-799R=0

a = 2; b = -799; c = 0;
Δ = b2-4ac
Δ = -7992-4·2·0
Δ = 638401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{638401}=799$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-799)-799}{2*2}=\frac{0}{4}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-799)+799}{2*2}=\frac{1598}{4}
=399+1/2
$