Theory:

A quadratic equation in the variable \(x\) is an equation of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), \(c\) are real numbers, \(a ≠ 0\). The degree of the quadratic equation is \(2\).
Important!
The equation \(ax^2 + bx + c = 0\) is called the standard form of a quadratic equation.
Example:
1. Check whether the equation \((x - 3)^2 + 2 = 3x - 4\) is a quadratic or not.
 
Solution:
 
\((x - 3)^2 + 2 = 3x - 4\)
 
\(\Rightarrow x^2 - 6x + 9 + 2 = 3x - 4\)
 
\(\Rightarrow x^2 - 6x + 11 - 3x + 4 = 0\)
 
\(\Rightarrow x^2 - 9x + 15 = 0\)
 
It is of the form \(ax^2 + bx + c = 0\).
 
Therefore, the given equation is a quadratic equation.
 
 
2. Check whether the equation \(x(x + 2) + 6 = x^2 - 3x + 4\) is a quadratic or not.
 
Solution:
 
\(x(x + 2) + 6 = x^2 - 3x + 4\)
 
\(\Rightarrow x^2 + 2x + 6 = x^2 - 3x + 4\)
 
\(\Rightarrow x^2 + 2x + 6 - x^2 + 3x - 4 = 0\)
 
\(\Rightarrow 5x + 2 = 0\)
 
Here, the degree of the equation is \(1\).
 
Therefore, the given equation is not a quadratic equation.