You need some further assumptions on $a$ to guarantee the existence of a solution to this equation, as there might not be solutions modulo some prime, say. The theorem of Hasse and Minkowski tells you exactly when solutions exist.

But anyway, the result you want is Theorem 8 in the paper: Heath-Brown - A New Form of the Circle Method, and its Application to Quadratic Form.

You can find this here: http://eprints.maths.ox.ac.uk/144/1/circle.pdf

You need some further assumptions on $a$ to guarantee the existence of a solution to this equation, as there might not be solutions modulo some prime, say. The theorem of Hasse and Minkowski tells you exactly when solutions exist.

But anyway, the result you want is Theorem 8 in the paper: Heath-Brown - A New Form of the Circle Method, and its Application to Quadratic Form.

You can find this here: http://eprints.maths.ox.ac.uk/144/1/circle.pdf (Wayback Machine)