2019 Mock AMC 10B Problems/Problem 7

Solution by excruciating: Subtracting $n$ from both sides gives $x^2-8x+(96-n^2)=0.$ For any quadratic $ax^2+bx+c$ , the sum of the roots is $-\frac{b}{a}.$ So, the sum of the roots is $-\frac{(-8)}{1} = \boxed{(A) 8}$ . Note that whatever $n$ is does not affect the sum of the roots.