32-18x-x^2=0

Solution for 32-18x-x^2=0 equation:

32-18x-x^2=0

We add all the numbers together, and all the variables

-1x^2-18x+32=0

a = -1; b = -18; c = +32;
Δ = b2-4ac
Δ = -182-4·(-1)·32
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{113}}{2*-1}=\frac{18-2\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{113}}{2*-1}=\frac{18+2\sqrt{113}}{-2}
$