SOLUTION: How to solve x^1/2-x^1/4-6=0 by substitution?

Introduce new variable u = .

Then your original equation takes the form

 = 0.

Factor left side:

(u-3)*(u+1) = 0.


Its roots are u= 3 and u= -2.

Since u = , you need only positive u = 3.

Then x =  = 81.


Answer.  x = 81.