Solution:

To find the value of k for which the quadratic equation 3x^2 - 5x + 2k = 0 has real equal roots, we need to consider the discriminant of the quadratic equation. The discriminant is given by the formula:

Discriminant (D) = b^2 - 4ac

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

In this case, the quadratic equation is 3x^2 - 5x + 2k = 0.

Comparing this equation with the standard form ax^2 + bx + c = 0, we can see that:
a = 3, b = -5, and c = 2k.

Now, substituting these values into the discriminant formula, we get:
D = (-5)^2 - 4(3)(2k)
= 25 - 24k
= -24k + 25

For real equal roots, the discriminant should be equal to zero. Therefore, we can set the discriminant equal to zero and solve for k:

-24k + 25 = 0
-24k = -25
k = -25/-24
k = 25/24

Hence, the value of k for which the quadratic equation has real equal roots is k = 25/24.

Summary:
- The discriminant of a quadratic equation determines the nature of its roots.
- To find the value of k for which the quadratic equation has real equal roots, we need to set the discriminant equal to zero.
- In this case, the discriminant is -24k + 25.
- Setting it equal to zero, we find k = 25/24.

6-10k=0
-10k=-6
10k=6
k=6/10
k=3/5