### 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.