Misc Formulas

The Quadratic Formula

$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

This is used to solve certain equations such as this:

$x^2-4x-7=0$

You replace all instances of b with the second number, -4.

$y=\frac{-(-4)\pm \sqrt{(-4{)}^2-4ac}}{2a}$

Then you replace all instances of a with the first number, which in this case is x², which means it is 1.

$y=\frac{-(-4)\pm \sqrt{(-4{)}^2-4(1)c}}{2(1)}$

Next you need to replace all instances of c with the third number, -7.

$y=\frac{-(-4)\pm \sqrt{(-4{)}^2-4(1)(7)}}{2(1)}$

Now simply reduce and solve.

$y=\frac{4\pm \sqrt{44}}{2}$

$y=\frac{4\pm \sqrt{4}\sqrt{11}}{2}$

Failed to parse (syntax error): {\displaystyle y= \frac{4\pm\2\sqrt{11}}{2}}

$y=2\pm \sqrt{11}$