User:Thomas Larsen/Sandbox

Example
To find the solutions to the equation $$x^2-6=x$$:



\begin{align} x &= x^2-6 \\ \therefore 0 &= x^2-x-6 \\ \text{Now } x &= \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \therefore a &= 1, b = -1, c = -6 \\ \therefore x &= \frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)} \\ \therefore x &= \frac{1\pm\sqrt{25}}{2} \\ &= \frac{1\pm5}{2} \\ \therefore x &= \frac{6}{2}=3 \text{ or } x = \frac{-4}{2}=-2. \end{align} $$