From your question, you want to ask for taking away of black? or the brown gold red?
If you want the black away (disapper) sooner, just wash it more.
Did you bleach your hair before you colored your hair to brown gold red? If you did bleach, after the black is gone, your hair will become gold. That is because when you bleach your hair, the black is gone from your hair and the color of brown and red can be gone by washing.
If you want your hair become black naturally, the only way you can do is to cut away all the gold hair.