Can I dye black over bright red?

About a month ago I dyed my hair a very bright red, and it was supposed to be permanent, but now it's faded to a (still bright) orange-y red. My natural hair is dark brown, and my roots are showing through. If I use a box dye (I don't have money to get it professionally done) will the black be in two tones -- dark on my roots, reddish on the red coloring (or will it even cover the red at all)? Or will it be just a solid black? Sorry if this is confusing -- thanks in advance.