Keep x as you defined it. Let y = number of expensive tickets bought for $1800. Then:

Cheap tickets: 1800 = (10 + y)x => 1800 = 10x + xy .... (1)

Expensive tickets: 1800 = y(x + 30) => 1800 = xy + 30y .... (2)

Equate (1) and (2): 10x + xy = xy + 30y => x = 3y .... (3)

Substitute (3) into (2): 1800 = 3y^2 + 30y => y^2 + 10y - 600 = 0 => (y + 30)(y - 20) = 0

etc.