Answer
No real solutions.
Work Step by Step
The given equation is
$x^2=3x-3$
Add $-3x+3$ to each side.
$x^2-3x+3=3x-3-3x+3$
Simplify.
$x^2-3x+3=0$
Graph the related function.
$f(x)=x^2-3x+3$
There are no $x-$ intercepts.
Hence, the equation has no real solutions.