Solve the equation x^2/5 + x^1/5 -6=0
don't let those fractional exponents confuse things. What you have is just
(x^1/5)^2 + x^1/5 - 6 = 0
That's just like
u^2+u-6=0
So, just factor it to be
(x^1/5 + 3)(x^1/5 - 2) = 0
x^1/5 = -3 or 2
x = -243 or 32