Answer
$(-\infty,-5)U(4,\infty)$ or $\{x|x\lt-5\ or\ x\gt4\}$.
Work Step by Step
Step 1. $x(x+1)\gt20 \longrightarrow x^2+x-20\gt0 \longrightarrow (x+5)(x-4)\gt0$.
Step 2. Identify boundary points $x=-5,4$ and form intervals $(-\infty,-5),(-5,4),(4,\infty)$.
Step 3. Choose test values $x=-6,0,5$ to test the inequality and get results $True,\ False,\ True$.
Step 4. Thus we have the solution $(-\infty,-5)U(4,\infty)$ or $\{x|x\lt-5\ or\ x\gt4\}$.
