**Solution:**

Let's solve the equation step by step to find the value of p.

**Step 1:**
Given equation: px^2 - 2√5px + 15 = 0

**Step 2:**
To determine if the equation has two equal roots, we need to find the discriminant (D) of the quadratic equation. The discriminant is given by the formula:

D = b^2 - 4ac

Where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

In our equation, a = p, b = -2√5p, and c = 15.

**Step 3:**
Substituting the values of a, b, and c into the discriminant formula:

D = (-2√5p)^2 - 4(p)(15)

**Step 4:**
Simplifying the expression:

D = 20p^2 - 4(15p)
D = 20p^2 - 60p

**Step 5:**
For two equal roots, the discriminant must be equal to zero.

Setting the discriminant equal to zero:

20p^2 - 60p = 0

**Step 6:**
Factoring out the common factor of 20p:

20p(p - 3) = 0

**Step 7:**
Using the zero-product property, we set each factor equal to zero:

20p = 0 or p - 3 = 0

**Step 8:**
Solving each equation:

For 20p = 0:
p = 0

For p - 3 = 0:
p = 3

**Step 9:**
Therefore, the values of p that satisfy the condition of the equation having two equal roots are p = 0 and p = 3.