To solve the equation 5x^2 - x = 18, we can rearrange it to the form 5x^2 - x - 18 = 0.

Now, we can factor the quadratic equation. The factors of 5x^2 are (5x)(x), and the factors of -18 are (-6)(3) or (6)(-3). We need to find the combination that adds up to -1x, which is -6 and 3.

So, the factored form of the equation is (5x - 6)(x + 3) = 0.

Now, we can set each factor equal to zero and solve for x:

5x - 6 = 0
5x = 6
x = 6/5

x + 3 = 0
x = -3

Therefore, the solutions to the equation 5x^2 - x = 18 are x = 6/5 and x = -3.