Find the values of k in the equation 6k2 = 5k + 6

A.

{\(\frac{-2}{3}, \frac{-3}{2}\)}

B.

{\(\frac{-2}{3}, \frac{3}{2}\)}

C.

{\(\frac{2}{3}, \frac{-3}{2}\)}

D.

{\(\frac{2}{3}, \frac{3}{2}\)}

Correct answer is B

6k2 = 5k + 6

6k2 - 5k - 6 = 0

6k2 - 0k + 4k - 6 = 0

3k(2k - 3) + 2(2k - 3) = 0

(3k + 2)(2k - 3) = 0

3k + 2 = 0 or 2k - 3 = 0

3k = -2 or 2k = 3

k = \(\frac{-2}{3}\) or k = \(\frac{3}{2}\)

k = (\(\frac{-2}{3}\), k = \(\frac{3}{2}\))