Documentation about filters in general
You can derive the expression for the coefficients by doing bilinear transformation of the following analog low-pass prototype filter

$$H(s) = \frac{w_0^2}{s^2 + (w_0/Q)s + w_0^2}$$

where $w_0$ is the cut-off frequency.

You can lookup the bilinear transformation on Wikipedia.

The filter used in the Android app is a Butterworth filter because the chosen value of Q is $1/\sqrt{2}$. Note that in the constructor the inverse of Q is computed and assigned to variable iQ which is used in the computation of the coefficients. Note also that the variable K holds the 'frequency-warped' value of the specified cut-off frequency. You can find more information about the frequency-warping phenomenon in the above link.

You can find many examples on digital filter design using bilinear transformation. I found this one, which is quite close to the Android example.