Evaluating a quartic polynomial.

[sid9221]

I want to find the root(for N) of this equation:

$$\frac{(2N-1)^2}{N(1-N)}=Ce^t$$

The hint says "consider taking a substitution u=N-1/2" ...which is the top bit of the fraction. But what does take a substitution here mean ?

This is a part of a loooong modelling problem which involved an ugly *** integral and gave this equation as the result. I've never evaluated a "quartic equation" so I'm a bit confused about the process.

I have the answer from wolfram so am looking for guidance on how to work it out by hand.

 

[DryRun]

$$\frac{(2N-1)^2}{N(1-N)}=Ce^t$$For the numerator, use the substitution:
$$2N-1=2u$$For the denominator, use the substitution:
$$N=\frac{2u+1}{2}$$

 

[Ray Vickson]

What is stopping you from substituting N = u + 1/2 into the expression on the left? It is simple algebra. If you actually DO it you will see how to proceed.

RGV