For what values of x is the quanity x2 + x – 20 negative

We need to solve the inequality

x² + x -20 > 0

In these cases, I usualy like to just set this up as an equality and find some "test" points !!!

So we have

x² + x -20 = 0    and factoring, we have

(x + 5) (x -4) = 0      and setting each factor to  0, we have that x = - 5  and x = 4

This tells us that the possible solutions come from these intervals (-∞, -5), (-5, 4) or (4,∞)...usually, in these quadratic inequalities, if the middle interval "works," the two "outside" intervals don't - or vice-versa !!!

Let's pick a point in the interval (-5, 4) and see if it "works" in the original problem - I always like "0"

So we have

(0)² + (0) - 20 > 0     and that clearly isn't true

So...my 'guess' is that the solutions come from the intervals (-∞, -5) and (4,∞)

Here's the graph of y = x² + x - 20

https://www.desmos.com/calculator/owbbudodv9

Ah......just as we suspected  !!!  ......the function is > 0 on (-∞, -5) and (4,∞)   !!!