0=X^2+32x-200

Solution for 0=X^2+32x-200 equation:

0=X^2+32X-200

We move all terms to the left:

0-(X^2+32X-200)=0

We add all the numbers together, and all the variables

-(X^2+32X-200)=0

We get rid of parentheses

-X^2-32X+200=0

We add all the numbers together, and all the variables

-1X^2-32X+200=0

a = -1; b = -32; c = +200;
Δ = b2-4ac
Δ = -322-4·(-1)·200
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{114}}{2*-1}=\frac{32-4\sqrt{114}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{114}}{2*-1}=\frac{32+4\sqrt{114}}{-2}
$