Factorials

Check your quadratic formula again. Here is the whole process:

$\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2a } \\ \\ \frac { 24\pm \sqrt { { 24 }^{ 2 }-4\times 1\times -1 } }{ 2\times 1 } \\ \\ \frac { 24\pm \sqrt { 580 } }{ 2 } \\ \\ \frac { 24\pm \sqrt { 4 } \sqrt { 145 } }{ 2 } \\ \\ \frac { 24\pm 2\sqrt { 145 } }{ 2 } \\ \\ 12\pm \sqrt { 145 }$

You would have got $\sqrt {143}$ if you did ${ 24 }^{ 2 }-4$ for the ${ b }^{ 2 }-4ac$ part. It is a double negative however, so you must be careful.