Let's rearrange the equation
#x^2-10x+21>0#
Let #f(x)=x^2-10x+21#
The domain of #f(x)# is #D_f(x) = RR#
Let's factorise
#f(x)=(x-3)(x-7)#
Now, we can establish the sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##3##color(white)(aaaaa)##7##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x-3##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-7##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#
Therefore,
#f(x)>0# when # x in ] -oo,3 [ uu ] 7, +oo[ #