To solve the equation X^2 - 5X = 14, we can first rewrite it in the standard form of a quadratic equation:

X^2 - 5X - 14 = 0

Next, we can factor the quadratic equation:

(X - 7)(X + 2) = 0

Setting each factor to zero, we find the solutions:

X - 7 = 0 or X + 2 = 0

X = 7 or X = -2

Therefore, the solutions to the equation X^2 - 5X = 14 are X = 7 and X = -2.