# Quadratic Equations A **quadratic equation** in a variable, say $x$, is an equation in which $x$ appears in terms only as $x^2$, as $x$, or not at all. A quadratic equation in $x$ can be rearranged to be of the form: $$ a x^2 + b x + c = 0 $$ where $a$, $b$, and $c$ do not involve $x$. ## Solutions The solutions -- if they exist -- of the quadratic equation $a x^2 + b x + c = 0$ are given by the **quadratic formula**: $$ x = \frac{ - b \pm \sqrt{b^2 - 4 a c }}{2 a} $$ [[!redirects quadratic formula]]