First, we can combine like terms:

(x^2 - x) - 14(x^2 - x) + 24
= x^2 - x - 14x^2 + 14x + 24
= -13x^2 + 13x + 24

Now, we have a quadratic equation in the form ax^2 + bx + c = 0 where a = -13, b = 13, and c = 24. We can solve this equation using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Plugging in the values, we get:

x = [-13 ± sqrt(13^2 - 4(-13)(24))] / 2(-13)
x = [-13 ± sqrt(169 + 624)] / -26
x = [-13 ± sqrt(793)] / -26

Therefore, the solutions are:

x = [-13 + sqrt(793)] / -26 and x = [-13 - sqrt(793)] / -26.