Answer
1
Work Step by Step
$3x(x-1)^\frac{1}{2}+2(x-1)^\frac{3}{2}=0$
$\sqrt {x-1}(3x+2(x-1)) = \sqrt {x-1}(5x-2)=0$
x=1 or 2/5
Checking the solutions in the original equation x=2/5 is extraneous.
(as x-1 should be >=0 for $\sqrt{x-1}$ to be defined)
