A carpenter is designing a table. The table will be in the form of a rectangle whose length is 4 feet more than its width. How long should the table be if the carpenter wants the area of the table to be 45 sq. ft ?

Let the width of the table be x feet.
Then, length of the table = (x + 4) ft
$$\eqalign{ & \therefore x\left( {x + 4} \right) = 45 \cr & \Rightarrow {x^2} + 4x - 45 = 0 \cr & \Rightarrow {x^2} + 9x - 5x - 45 = 0 \cr & \Rightarrow x\left( {x + 9} \right) - 5\left( {x + 9} \right) = 0 \cr & \Rightarrow \left( {x + 9} \right)\left( {x - 5} \right) = 0 \cr & \Rightarrow x = 5 \cr} $$
Hence, length of the table = (5 + 4) = 9 feet