Question 55036
x^2-5x-14>0
Factor to get:
(x-7)(x+2)>0
Draw a line; put the numbers -2 and 7 on it.
This creates three intervals: (-inf,-2),(-2,7),(7,+inf)
Check a number in each interval to see where the solutions
for your problem lie, as follows:
Interval I: choose -10; (-10-7)(-10+2)>0 so this interval is part of the solution set.
Interval II: choose 0: (0-7)(0+2)<0 so no solutions here.
Interval III: choose 10: (10-7)(10+2)>0 so this interval is part of the
solution set.
SOLUTION: 
-inf<x<-2 OR 7<x<+inf
Cheers,
Stan H.