You can put this solution on YOUR website! Let the first be x. The next is x+1.
So we have
x(x+1) = 90
x^2 + x - 90 = 0
(x + 10)(x - 9) = 0
x = -10 or x = 9
x+1 = -9 or x+1 = 10
but since the question asked for negative integers, the numbers you want are -10 and -9