Generalised method :
 Consider the quadratic equation ${ax^2 + bx + c = 0}$ ${(a ≠ 0)}$. Dividing throughout by ${a}$ we get:
  ${x^2 + b/ax + c/a = 0}$
  Converting it in the form of perfect sqaure i.e ${(x-a)^2-b^2=0}$ or ${(x+a)^2-b^2=0}$
  ${(x+1/2b/a)^2-(1/2b/a)^2 +c/a = 0}$
  ${(x+b/(2a))^2 - (b^2-4ac)/(4a^2) = 0}$
  So, the roots of the given equation are the same as those of 
   ${[x+b/(2a)]^2 - (b^2-4ac)/(4a^2) = 0}$                             (1)
   
Case 1:   If b2  – 4ac ≥ 0, then by taking the square roots in (1), we get
   ${[x+b/(2a)]= ±√(b^2-4ac)/(2a)}$
    $x={-b±√{b^2-4ac}}/{2a}$
	
So, the roots of ${ax^2  + bx + c = 0}$ are  $x={-b+√{b^2-4ac}}/{2a}$ and  $x={-b-√{b^2-4ac}}/{2a}$

Case 2: If ${b^2  – 4ac < 0}$, the equation will have no real roots. 

This formula for finding the roots of a quadratic equation is known as the quadratic formula.

Example: The area of a rectangular plot is 528 ${m^2}$. The length of the plot (in metres) is one more 
than twice its breadth. We need to find the length and breadth of the plot.Solve using quadratic formula.

Solution:
Let the breadth of the plot be $x$ metres.
Then the length is $(2x + 1)$ metres. Then we are given that ${x(2x + 1) = 528}$, 
i.e., ${2x^2  + x – 528 = 0}$.
This is of the form ${ax^2  + bx + c = 0}$, where ${a = 2}$, ${b = 1}$, ${c = – 528}$.
Since quadratic formula is given by the equation:
 $x={-b±√{b^2-4ac}}/{2a}$
 Therefore $x={-1±√{1^2-4(2)(-528)}}/{2(2)}$
             =${-1±√4225}/{4}$
			 =${-1±65}/{4}$
Therefore the solutions of the equations are 
            ${x=64/4}$  or  ${x=-66/4}$ 
		i.e ${x=16}$  or  ${x=-33/2}$
Answer: Since  $x$  cannot  be  negative,  being  a  dimension,  the  breadth  of  the  plot  is
16 metres and hence, the length of the plot is 33 meters.