please confirm the question is x = (-7x^2 - 1) / (x + 4)
if that is the case, then
x * (x + 4) = -7x^2 - 1
x^2 + 4x = -7x^2 -1
8x^2 + 4x + 1 = 0
which does not have any real solution
Edit - much easier question to evaluate the expression (x^2 -1) / (x + 4) when x=-7
(-7^2 - 1) / (-7 + 4)
= (49 -1 ) / -3
= 48 / -3
= -16