You can't have a line break in an equation environment, so the \\ does nothing.
A better way to type the equation could be
\begin{equation}
B_{1} = 0.9\,B_{2} + \Bigl[
\sqrt{(x_{1}^2 + y_{1}^2 + z_{1}^2)}-
\sqrt{(x_{2}^2 + y_{2}^2 + z_{2}^2)} \; \Bigr]
\end{equation}
so that the various components of the equation are more visible.
I've made a couple of changes:
\Bigl[ for the opening bracket and \Bigr] for the closing one (as \bigg size seems too much). Notice the final l or r to declare the type of delimiter;
a thin space \, between the decimal number 0.9 and B_{2} (which I wouldn't put in parentheses), as the result of 0.9B_{2} might be confusing;
a thick space between the second square root and the closing bracket for symmetry with the space at the start.
There is no special way to mark B_{1}: it's just a symbol with a subscript.
