Try a second example. This one is a lot harder. We want the wavelength this time, not the speed.

Suppose a galaxy (or any other object) is moving away with a speed of 100 km/s. To what wavelength is the H alpha line shifted to?
[assume the rest wavelength of H alpha is 656.25 nm]

Solution:
Doppler's Law:
v = c * (lambda - lambda_rest) / lambda_rest
where
v = 100 km/s,
lambda_rest = 656.25 nm , and of course, c=3x10⁵ km/s

So to get the wavelength (lambda), we need to separate it from all the other parts. First, let's bring c from the right hand side to the left hand side:
(v/c) =(lambda - lambda_rest) / lambda_rest

Now let's bring lambda_rest from the denominator on the right to the left hand side:
(v/c) * lambda_rest = (lambda - lambda_rest)

We are almost there!. The final step is to bring lambda_rest from the right to the left:
{(v/c) * lambda_rest } + lambda_rest = lambda
Now we have the expression we need to calculate lambda. So plug in the values:
{ ((100 km/s / (3x10⁵ km/s)) * 656.25 nm } + 656.25 nm = lambda
656.46875 nm = lambda, or
The observed wavelength of the galaxy is at a wavelength of lambda = 656.47 nm.

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Ok, for those of you who want a challenge:

Why should the redshift really be called a redstretch?