-x2+x+72>0

Solve -x^2 + x + 72 > 0.

• Factor: -x^2 + x + 72 = -(x^2 - x - 72) = -(x - 9)(x + 8).
• So -(x - 9)(x + 8) > 0 implies (x - 9)(x + 8) < 0.
• The product of two numbers is negative between their roots, i.e., for -8 < x < 9.

Check endpoints: at x = -8 or x = 9, the expression is 0, not allowed.

Solution: -8 < x < 9.