#### Answer

$x=17$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
3\sqrt{x-1}=2\sqrt{2x+2}
,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation.
$\bf{\text{Solution Details:}}$
Squaring both sides of the equation results to
\begin{array}{l}\require{cancel}
\left( 3\sqrt{x-1} \right)^2=\left( 2\sqrt{2x+2} \right)^2
\\\\
9(x-1)=4(2x+2)
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
9(x)+9(-1)=4(2x)+4(2)
\\\\
9x-9=8x+8
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
9x-8x=8+9
\\\\
x=17
.\end{array}
Upon checking, $
x=17
$ satisfies the original equation.