Calculate the discriminant and use it to determine how many real-number roots the equation has
3x^(2)-6x+4=0

The quadratic formula is:

x=(-b±√(b^2-4ac))/(2a) for the quadratic of the form ax^2+bx+c

The discriminant is the (b^2-4ac) part of the quadratic formula.

Let d=(b^2-4ac).  If:

d<0:  There are no real roots.

d=0:  There is one real root.

d>0:  There are two real roots.

In this case the discriminant is:

(-6)^2-4*3*4

36-48

-12

Since -12<0 there are no real roots for the equation 3x^2-6x+4.