We must first find the roots of the quadratic equations
#x^2-2x-4=0#
The discriminant is
#Delta=b^2-4ac=(-2)^2-4*(1)*(-4)=20#
As #Delta>0#, there are #2# real roots
The roots are
#x=(-b+-sqrtDelta)/(2a)#
#x_1=(2-sqrt20)/2=1-sqrt5#
#x_2=(2+sqrt20)/2=1+sqrt5#
Let #f(x)=x^2-2x-4#
We can build the sign chart
#color(white)(aaaa)##x##color(white)(aaaaaa)##-oo##color(white)(aaaa)##x_1##color(white)(aaaa)##x_2##color(white)(aaaa)##+oo#
#color(white)(aaaa)##(x-x_1)##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##(x-x_2)##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#
Therefore,
#f(x)>0# when #x in (-oo, (1-sqrt5)) uu((1+sqrt5), +oo)#