(х+2) (19-х)-х (18-х)=30

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Expanding the terms within parentheses, we get:

(х + 2)(19 - х) - х(18 - х) = 30

Now, multiply the terms within each set of parentheses:

(х19 - х^2 + 219 - 2х) - (18х - х^2) = 30

Simplify by combining like terms:

19х - х^2 + 38 - 2х - 18х + х^2 = 30

-x^2 - х= 30

Rearranging the equation:

x^2 + x - 30 = 0

Now, we need to solve this quadratic equation. The solutions are:

x = -6 or x = 5

Therefore, the solutions to the original equation are x = -6 and x = 5.