Derivation of formula used in calculating molecular mass from a mixture
Hint: $$v_{rms}=\sqrt{\frac{3RT}M}$$

And weighted average of speeds for mixture.

EDIT:

$$ v_{mix} ^{rms}= x_1 v_1^{rms}+ x_2 v_2^{rms}$$ 

This will complete the derivation of the formula you gave.