a. The width of the dining area is x+15+x; the length is x+10+x. The area (=length*width) must be 1800. That gives us the following equation:
(2x+15)(2x+10) = 1800 => 4x² + 50x + 150 = 1800 =>
4x² + 50x - 1650 = 0
Put 4, 50 and -1650 in the quadratic formula to find x=15 (or x=-27.5 but that is not applicable to this real-world problem).
b. width = 2x+15 = 45, length = 2x+10 = 40