Solving Logistic Equation Homework Problem

[roam]

Homework Statement

I'm having some difficulty understanding the last step of the following solved problem from my textbook:

We will compute the equilibrium points of kP \left( 1- \frac{P}{N} \right) - C.

kP \left( 1- \frac{P}{N} \right) - C =0

-kP^2+kNP - CN =0

The quadratic equations has solutions

P= \frac{N}{2} \pm \sqrt{\frac{N^2}{4}-\frac{CN}{k}}

The Attempt at a Solution

So if we start off by

-kP^2+kNP - CN =0

and using the quadratic equation:

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

I get:

P= \frac{-kN \pm \sqrt{(kN)^2-4kC}}{2k}

= \frac{N}{2} \pm \frac{\sqrt{k^2N^2-4kC}}{2k}

So, why is my answer different from the one in the textbook? And how can I end up with the solution in the book (that I've posted above)?

 

[scurty]

P= \frac{-kN \pm \sqrt{(kN)^2-4kC}}{2k}

= \frac{N}{2} \pm \frac{\sqrt{k^2N^2-4kC}}{2k}

2k = \sqrt{\text{(what?)}}

 

[roam]

2k = \sqrt{\text{(what?)}}

Oh, I see. I never thought of it. Thank you very much.