6.4.. Unless you need it in a fraction..
6x = n²-16
n²-6x-16=0 -16=-8*2, -6=-8+2
(n-8)(n+2)=0
n-8=0, n+2=0
n=8, n=-2
Negative solution is -2.
<h2><u><em>GLAD YOU FOUND YOUR ANSWER!!!!!!</em></u></h2>
Given is the number of science fiction books = 48
Let the number of mystery books be = x
Let the number of biographies be = y
Ratio of the number of mystery books to the number of science fiction books is 4:3 so
=

Ratio of the number of science fiction books to the number of biographies is 4:5 so 
=

Hence there are 48 science fiction books, 64 mystery books and 60 biographies.
So total number of books are = 