3x (x-1) ^1/2 + 2 (x-1) ^3/2 = 0 solve

x = 827

and

Neg 1

Factor out the neg first then you will get that out the way

3x (x - 1) ^1/2 + 2 (x - 1) ^3/2 = 0

Factoring:-

(x - - 1) ^1'2 (3x + 2 (x - 1) = 0

therefore

(x - 1) ^1/2 = 0 or (5x - 2) = 0

x = 1 or x = 2/5

There is one real root 1 as 2/5 will not give a real root (0.5-1) ^ (1/2) is not real.