Definition of Quadratic Equation
A quadratic equation is an equation that can be written in a form like this: ax^{2} + bx +c = 0. In this equation, a, b, and c are constant numbers. The numbers a and b are called coefficients because they are multiplied with x. X is a variable. The equation can be written in different ways, such as ax^{2} = bx – c, but simply rearranging the equation doesn’t change the fact that it is a quadratic equation.
Standard Form
An equation of the form ax^{2} + bx +c = 0,
 where a,b,c are real numbers
 and a ≠ 0
is called a quadratic equation in x.
Quadratic Equation Example:
Root of a Quadratic Equation: A real number k is called a root of the Quadratic Equation ax^{2} + bx +c = 0, a ≠ 0 If ak^{2} + bk +c = 0.
Note 1: if k is a root of ax^{2} + bx +c = 0, then we say that
 X=k satisfies the equation ax^{2} + bx +c = 0 or
 X=k is a solution of the equation ax^{2} + bx +c = 0.
Note 2: The roots of a Quadratic Equation ax^{2} + bx +c = 0 are called the zeros of the polynomial ax^{2} + bx +c .
Here are some examples:
2x^{2} + 5x + 3 = 0  In this one a=2, b=5 and c=3  
x^{2} − 3x = 0  This one is a little more tricky:


Quadratic formula
How do I solve a quadratic equation?
you can solve for x if you know the values of a, b and c.
When you solve a quadratic equation with the quadratic formula, you will always find two solutions. That is because there are always two values of x that satisfy the conditions of the quadratic formula. So you will never find exactly one solution. However, not all solutions are real numbers. When you calculate your solution to your quadratic equation, you might find that you have:
 two real number solutions,
 or, two solutions, both of which are complex numbers.