How do I calculate principal quantum numbers of the Lyman series

How do I calculate principal quantum numbers of the Lyman series?


I've been given that the lowest line is 121.6nm and the 5th line is 93.8nm


The formula of the wavenumber is v=-R(1/n2^2 - 1/n1^2)


My taught was that as the wavenumber is known (1/wavelength) I could create an equation


v/-R = 1/(x+4)^2 - 1/x^2 and solve for x to get the principal quantum numbers


However this equation seems to be too hard to solve and I guess there is a different way to solve this.


Many thanks in advance


