Does |x^2-3x+3|=3 have a solution?

Question

My answer was that there isn't a solution.
Am i right?

Answer 1

The left side can be -3 or 3 since the absolute value of -3 is 3.

Therefore this can be split in to 2 equations:
x^2-3x+3=3
Which simplifies to,
x^2-3x=0

and,

x^2-3x+3=-3
Which simplifies to,
x^2-3x+6=0

Try to solve these and check the discriminant to find the possible solutions.