R(p)=2500p-175p2

Solution for R(p)=2500p-175p2 equation:

(R)=2500R-175R^2

We move all terms to the left:

(R)-(2500R-175R^2)=0

We get rid of parentheses

175R^2-2500R+R=0

We add all the numbers together, and all the variables

175R^2-2499R=0

a = 175; b = -2499; c = 0;
Δ = b2-4ac
Δ = -24992-4·175·0
Δ = 6245001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6245001}=2499$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2499)-2499}{2*175}=\frac{0}{350}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2499)+2499}{2*175}=\frac{4998}{350}
=14+7/25
$