Answer
Discriminant = -8; 2 solutions that are not real but complex
Work Step by Step
$3x^2=2x-1$
$3x^2-2x+1=0$
Plug the coefficients into the discriminant of the quadratic formula.
$a=3, b=-2, c=1$
$\sqrt {b^2-4ac}$
$\sqrt {(-2)^2-4(3)(1)}$
$\sqrt {4-12}$
$\sqrt {-8}$
Since the discriminant is less than $0$, the equation has two solutions that are not real but complex.