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}}

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