A quadratic equation is a polynomial of degree two. Its general form is $ax^2+bx+c=0$ where $$a\neq0$$. It can be solved to find $$x$$ in 3 main ways:

Factorising

Click on one of the above links to find out more and see worked examples.

A solution of a quadratic equation is often also called a "root". Click here to find out about how the discriminant can be used to find out how many roots any given equation has.

What is a root of an equation?

For a given quadratic equation $y=ax^2+bx+c$ we can sketch the graph. Take the equation $y=x^2-1$ The graph looks like the one shown here:
A root is found when $$y=0$$. With $$y$$ being the vertical axis, this simply means "when the graph intersects the $$x$$ axis". The roots are highlighted in this image, you may notice that the $$y$$ coordinate is $$0$$ in both, by the definition of a root. The $$x$$ coordinates are found through one of the above 3 methods.