-x^2-24x+32=0

Solution for -x^2-24x+32=0 equation:

-x^2-24x+32=0

We add all the numbers together, and all the variables

-1x^2-24x+32=0

a = -1; b = -24; c = +32;
Δ = b2-4ac
Δ = -242-4·(-1)·32
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{11}}{2*-1}=\frac{24-8\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{11}}{2*-1}=\frac{24+8\sqrt{11}}{-2}
$