R(x)=x(12-(x/1000))

Solution for R(x)=x(12-(x/1000)) equation:

(R)=R(12-(R/1000))

We move all terms to the left:

(R)-(R(12-(R/1000)))=0

We add all the numbers together, and all the variables

R-(R(12-(+R/1000)))=0

We multiply all the terms by the denominator


R*1000)))-(R(12-(+R=0

We add all the numbers together, and all the variables

R+R*1000)))-(R(12-(=0

Wy multiply elements

1000R^2+R=0

a = 1000; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1000·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*1000}=\frac{-2}{2000}
=-1/1000
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1000}=\frac{0}{2000}
=0
$