How do you check a reciprocal quadratic equation?

Question

I did manage to figure out one (I believe anyhow) but I'm not quite sure how to check it.

x^-2 + x^-1 -6 = 0

Now, I've deduced that the answers are x= -1/3 and 1/2, but I'm not feeling confident on how I've plugged them in to check.

Answer 1

Solution:
Multiply by x^2 to get
1 + x - 6x^2 = 0
=> 6x^2 - x - 1 = 0
=> (3x + 1)(2x - 1) = 0
=> x = - 1/3 or x = 1/2
-----------------------------------------------------------------------------------
Verification:
(-1/3)^(-2) + (-1/3)^(-1) -6
= (-3)^2 + (-3) - 6
= 0

(1/2)^(-2) + (1/2)^(-1) - 6
= (2)^2 + (2) - 6
= 0.

Answer 2

1/(-1/3)^2 + 1/(-1/3) - 6 =? 0
1/(1/9) - 1/(1/3) - 6 =? 0
9 - 3 - 6 = 0

1/(1/2)^2 + 1/(1/2) - 6 =? 0
1/(1/4) + 1/(1/2) - 6 =? 0
4 + 2 - 6 = 0