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.
