To solve this equation, we need to first simplify the expression on the left side and then solve for x.

Given equation: (5x^2 - 36) / 6x = x - 2

First, simplify the left side by factoring out a common factor in the numerator:

5x^2 - 36 = 5(x^2 - 6^2) = 5(x + 6)(x - 6)

Now, substitute this back into the equation:

(5(x + 6)(x - 6)) / 6x = x - 2

Now, we can cancel out common factors to simplify further:

(5(x + 6)(x - 6)) / 6x = x - 2
(5(x + 6)(x - 6)) / 6x = 6x / 6x - 2

Next, we can cross multiply to get rid of the fractions:

5(x + 6)(x - 6) = 6x^2 - 12x
5(x^2 - 36) = 6x^2 - 12x
5x^2 - 180 = 6x^2 - 12x

Now, rearrange the terms to set the equation to zero:

6x^2 - 5x^2 - 12x + 180 = 0
x^2 - 12x + 180 = 0

Now, we have a quadratic equation. We can solve this by factoring or using the quadratic formula. The factored form would be:

(x - 6)(x - 30) = 0

Setting each factor to zero gives us two solutions:

x - 6 = 0 or x - 30 = 0

x = 6 or x = 30

Therefore, the solutions to the equation are x = 6 or x = 30.