The quadratic equation (k+1)x^2 + (5k-3)x + 3k = 0 has equal roots, find the possible values of the real number k.

Given that the equation is quadratic and has two distinct roots , this implies that the discriminant (b² - 4ac) in the quadratic formula is equal to zero. Comparing terms a = (k+1), b = (5k -3) and c = 3k, so b² - 4ac = (5k - 3)² - 4 (k+1)(3k) = 0. Multiplying out this gives: 13k² - 42k + 9, which is another quadratic equation this time in terms of the variable k. Solving this quadratic by inspection or using the quadratic formula k = 3 or k = 3/13.