Speed of sound in a gas mixture

Rick4

In a mixture of argon (atomic mass = 39.9 u) and neon (atomic mass = 20.2 u), the speed of sound is 363 m/s at 300K. Assume that both monatomic gases behave as ideal gases. Find the percentage of the atoms that are argon and the percentage that are neon.

I found the solution (in the attachments) but what I can't figure out is where the equation that was used in step 4 of the solution came from.

This is the equation that was used to solve the problem.
Where did it come from?

v = (v₁v₂(V₁+ V₂)^1/2)/(V₂v₁² + V₁v₂²)^1/2

Attached Thumbnails