R(p)=5p^2+1850p

Solution for R(p)=5p^2+1850p equation:

(R)=5R^2+1850R

We move all terms to the left:

(R)-(5R^2+1850R)=0

We get rid of parentheses

-5R^2+R-1850R=0

We add all the numbers together, and all the variables

-5R^2-1849R=0

a = -5; b = -1849; c = 0;
Δ = b2-4ac
Δ = -18492-4·(-5)·0
Δ = 3418801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3418801}=1849$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1849)-1849}{2*-5}=\frac{0}{-10}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1849)+1849}{2*-5}=\frac{3698}{-10}
=-369+4/5
$