For those values of "k" for which the discriminant  d = b^2 - 4ac  is positive 

    (I refer to the general form of quadratic equation  ax^2 + bx + c = 0.)


In your case the discriminant is  k^2 -4*2*(-3) = k^2 + 24.


This expression is positive for all and any values of "k": it is the sum of a square and the positive number.


Hence, the given equation has 2 (two) different real solutions at any value of k.