The length and width of a rectangle are consecutive even integers. the area of the rectangle is 80 square units. what are the length and width of the rectangle?

X(x + 2) = 120sq units 

Set it equal to 0 
x^2 + 2x - 120 = 0 

factor 
(x + 12)(x - 10) 

For the shorter side: 
x - 10 = 0 
x = 10 

Now that you have x, solve for the longer side which we said was represented by 
x + 2 
10 + 2 = 12 

Proof 
A = L x W 
120 = 10 x 12 
120 = 120 
true 

Our length is 12 and our width is 10