[Sonitex]

Problem statement:
The visible emission lines observed by Balmer all involved n_f = 2
(a) Explain why only the lines with n_f = 2 were observed in the visible region of the electromagnetic spectrum.

(b) Calculate the wavelengths of the first three lines in the Balmer series-those for which n_i = 3,4, and 5.

Attempt at solution:
I know that when and electron jumps from a higher energy level to a lower energy level, that it emits photons which is responsible for the lines in the spectra. However, I start to get lost in the textbook when Bohr comes in with his equation:
ΔE=hv = hc/λ = (-2.18 x 10^-18 J) x (1/n²_f - 1/n²_i)

Then it continues with λ= c/ν = hc/ΔE to calculate the wavelength with the energy calculated from the previous equation.

[Corribus]

It's not clear where you're getting your equation and values from. 
The generalized Rydberg equation can be found here:

https://en.wikipedia.org/wiki/Rydberg_formula

Just be careful with units and it's pretty much plug-and-chug.