R(p)=-59p^2+65p

Solution for R(p)=-59p^2+65p equation:

(R)=-59R^2+65R

We move all terms to the left:

(R)-(-59R^2+65R)=0

We get rid of parentheses

59R^2-65R+R=0

We add all the numbers together, and all the variables

59R^2-64R=0

a = 59; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·59·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*59}=\frac{0}{118}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*59}=\frac{128}{118}
=1+5/59
$