Question

What multiplies to 24 and adds to -9

Answer 1

Unfortunately, there are no two such numbers.

If your original question was: $\sf{x^{2} -9x+24=0}$ and you were trying to factor it, I would suggest the quadratic formula.

There are two solutions to $\sf{ax^2+bx+c=0$, where $\sf{a\neq 0}$, and we can find them by using the quadratic formula: 

$\huge{\sf{x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}}}$

So using that, here is how it would get factored:

For your equation, $\sf{a = 1, b = -9, c = 24}$

Plug in those values into the formula:

$\sf{\frac{ -(-9) \pm \sqrt{ (-9)^2 - 4 \cdot 1 \cdot 24} }{ 2 \cdot 1 }}$

Simplifying it:

$\sf{\frac{ 9 \pm \sqrt{ -15 } }{ 2 }}$

And so the solutions are:

$\sf{x_1 = \frac{ 9~+~\sqrt{ -15 } }{ 2 } = \frac{9}{2}+\frac{1}{2}\sqrt{15}i}$
and
$\sf{x_2 = \frac{ 9~-~\sqrt{ -15 } }{ 2 } = \frac{9}{2}-\frac{1}{2}\sqrt{15}i}$

Answer 2

No pair of real numbers can do that job.

When you learn about imaginary and complex numbers,
you'll be able to answer the question on your own.  The
two numbers are ...

         -4.5 + i √3.75
and
         -4.5 - i √3.75