x^1/2 - 7x^1/4 + 12 = 0

let x^(1/4) = k

then we have
k^2 - 7k + 12 = 0
(k-3)(k-4) = 0
k = 3 or k = 4
x^(1/4) = 3 or x^(1/4) = 4
x = 81 or x = 256