Finding Minimum Value for Quadratic Equation Discriminant

Consider the quadratic equation given by:

$$2x^2 - 4x + k = 0$$

where $k$ is a constant. This equation has two distinct real solutions if and only if the discriminant is positive. Recall that the discriminant for a quadratic equation of the form $ax^2 + bx + c = 0$ is calculated as:

$$D = b^2 - 4ac$$

Using the specific values from the equation, determine the minimum value of $k$ such that the equation has two distinct real solutions.