Quadratic Equation
This is a Quadratic Equation: 

(a, b, and c can have any value, except that a can't be 0.) 
 The letters a, b and c are the coefficients (you know these)
 The letter "x" is the variable or unknown (you don't know it yet)
 (See Basic Algebra Definitions)


The name Quadratic comes from "quad" meaning square, because the highest exponent is a square (in other words x^{2}).

Examples of Quadratic Equations:


In this one a=2, b=5 and c=3 





This one is a little more tricky:
 Where is a? In fact a=1, because we don't usually write "1x^{2}"
 b=3
 And where is c? Well, c=0, so is not shown.



Oops! This one is not a quadratic equation, because it is missing x^{2} (in other words a=0, and that means it can't be quadratic) 
Why is it special?
Quadratic equations can be solved using a special formula called the Quadratic Formula:
Solving
To solve, just plug the values of a, b and c into the Quadratic Formula, and do the calculations.
Example: Solve 5x² + 6x + 1 = 0
Quadratic Formula: x = [ b ± √(b^{2}4ac) ] / 2a
Coefficients are: a = 5, b = 6, c = 1
Substitute a,b,c: x = [ 6 ± √(6^{2}4×5×1) ] / 2×5
Solve: x = [ 6 ± √(36^{}20) ]/10 = [ 6 ± √(16) ]/10 = ( 6 ± 4 )/10
Answer: x = 0.2 and 1
(Check:
5×(0.2)² + 6×(0.2) + 1 = 5×(0.04) + 6×(0.2) + 1 = 0.2 1.2 + 1 = 0
5×(1)² + 6×(1) + 1 = 5×(1) + 6×(1) + 1 = 5  6 + 1 = 0)
Quadratic Equation In Disguise
Some equations may not look like quadratic equations, but with a little clever work they can be made into one:
In disguise 
What to do 
In standard form 
a, b and c 
x^{2} = 3x 1 
Move all terms to left hand side 
x^{2}  3x + 1 = 0 
a=1, b=3, c=1 
2(x^{2}  2x) = 5 
Expand (undo the brackets), and move 5 to left 
2x^{2}  4x  5 = 0 
a=2, b=4, c=5 
x(x1) = 3 
Expand, and move 3 to left 
x^{2}  x  3 = 0 
a=1, b=1, c=3 
5 + 1/x  1/x^{2} = 0 
Multiply by x^{2} 
5x^{2} + x  1 = 0 
a=5, b=1, c=1 
