We have to solve the inequatity: x^4 - 32x^2 - 144 > 0

x^4 - 32x^2 - 144 > 0

=> x^4 - 36x^2 + 4x^2 - 144 > 0

=> x^2(x^2 - 36) + 4(x^2 - 36) > 0

=> (x^2 + 4)(x^2 - 36) > 0

For this to be true either both (x^2 + 4) > 0 and (x^2 - 36)> 0 or (x^2 + 4) < 0 and (x^2 - 36) < 0

(x^2 + 4) > 0 and (x^2 - 36)> 0

=> x^2 > -4 and x^2 > 36

=> x^2 > 36

=> x > 6 or x < -6

(x^2 + 4) < 0 and (x^2 - 36) < 0

=> x^2 < -4 and x^2 < 36

=> x^2 < -4

This gives complex roots for x.

**The real solutions of the inequality are (-inf., -6)U(6, inf.)**