Find the values of k for which the equation (2k-3)x^2 - kx + (k-1) = 0

A quadratic equation has two equal roots when its discriminant is equal to 0. Calculating the discriminant of the given equation: D = k² - 4(k-1)(2k-3) = k² - 8k²+20k-12 = -7k²+20k-12=0 Solving this equation for k: 7k²-20k+12=0 D = 100-84 = 16 k_1,2=(10+-4)/7 => k = 6/7, k=2