x for the length,

(x-5) for the width.


The area equation is


    x*(x-5) = 300.


It is your basic equation to be solved.


Reduce it to the standard form of a quadratic equation


    x^ 2 - 5x - 300 = 0     (*)


From this point, you can solve this equation in 2 (two) ways.


One way is to apply the quadratic formula


     =  =  = ,


which gives you two roots x=  =  = 20  and  x =  =  = -15.


Of these two roots, only positive x = 20 makes sense.



The other way to solve quadratic equation (*) is to factor its left side

    (x-20)*(x+15) = 0.


It gives the same two roots, of which you chose the positive value x= 20.


So, your ANSWER is: the length of the pool is 20 feet.