*dont care much for the answer as much as the work*
solve x^2-8x-48=0

In form
ax²+bx+c=0
when a=1

fine what 2 numbers multiply to get c and add to get b

so

x²-8x-48=0
what 2 numbres multiply to get -48 and add to get -8
-12 and 4
(x-12)(x+4)=0
set equal to zero each factor

x-12=0
x=12

x+4=0
x=-4

x=-4 or 12