Calculate Luminosity of Vega
The $b$ in your equation, brightness, is what we call a "Flux".  That's the amount of energy per unit area at a certain distance.  Flux can be calculated using the Stefan-Boltzmann law.
$$
J=\sigma T^4
$$
where $\sigma=5.670373\times10^{-8}\space W\space m^{-2}\space K^{-4}$is the Stefan-Boltzmann constant, This is measured in Watts per square meter.  That means that we will need our distance to be in meters, and we will get a luminosity in Watts.  We can go a little further and divide our answer by $3.828\times10^{26} \space W$ to get our final value in solar luminosities (L$_\odot$).

That will make our final equation:
$$
L=\frac{4\pi R^2 \sigma T^4}{L_\odot}
$$
Because we're using the Stefan-Boltzmann equation, instead of the distance to the star, we have to use its radius.  Vega's radius is $2.362 \space R_\odot$, which is $1.64\times10^9$ meters. Its surface temperature is 9,600 K.  Plugging in those numbers yields a luminosity of:
$$
L=42.7L_\odot
$$
This value is slightly different from the value quoted by Wikipedia, due to rounding, but is well within the acceptable range.