For the quadratic equation 2x2 − 6x + 3a = 0, find the value of a that results in equal roots.

For a quadratic equation $Ax^2 + Bx + C = 0$ to have equal roots, the discriminant must be zero.
The discriminant is given by $\Delta = B^2 - 4AC$.

The given quadratic equation is $2x^2 - 6x + 3a = 0$.
Comparing this to $Ax^2 + Bx + C = 0$, we have:
$A = 2$
$B = -6$
$C = 3a$

Set the discriminant to zero:

The value of $a$ for which the quadratic equation has equal roots is $\frac{3}{2}$.

The correct option is D.