Square both sides.
\[3x+2\sqrt{2x(x-3)}-3=1\]
Separate terms with roots from terms without roots.
\[2\sqrt{2x(x-3)}=1-3x+3\]
Simplify \(1-3x+3\) to \(-3x+4\).
\[2\sqrt{2x(x-3)}=-3x+4\]
Square both sides.
\[8x(x-3)=9{x}^{2}-24x+16\]
Expand.
\[8{x}^{2}-24x=9{x}^{2}-24x+16\]
Cancel \(-24x\) on both sides.
\[8{x}^{2}=9{x}^{2}+16\]
Subtract \(9{x}^{2}\) from both sides.
\[8{x}^{2}-9{x}^{2}=16\]
Simplify \(8{x}^{2}-9{x}^{2}\) to \(-{x}^{2}\).
\[-{x}^{2}=16\]
Multiply both sides by \(-1\).
\[{x}^{2}=-16\]
Take the square root of both sides.
\[x=\pm \sqrt{-16}\]
Simplify \(\sqrt{-16}\) to \(\sqrt{16}\imath \).
\[x=\pm \sqrt{16}\imath \]
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[x=\pm 4\imath \]
x=4*IM,-4*IM
