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How to solve a quadratic equation?

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A quadratic equation is an equation of the form
$$ax^2 + bx + c = 0   \tag{1} $$
$ a,b,c \in \mathbb{R}$ and $a \ne 0 $.
Let us assume that we are trying to solve this equation for real numbers only.
The value
$$D = b^2 - 4ac  \tag{2} $$
is called discriminant of the equation $(1)$.
Case #1:
When $D \gt 0$, there are two distinct real solutions to $(1)$ and they are:
$$x_{1,2} = {-b \pm \sqrt{b^2-4ac} \over 2a} \tag{3} $$
Case #2:
When $D = 0$, there is one real solution to $(1)$ which is:
$$x = {-b \over 2a} \tag{4} $$
Case #3:
When $D \lt 0$, there are no real solutions to $(1)$.

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