x2+32x-200=0

Solution for x2+32x-200=0 equation:

x2+32x-200=0

We add all the numbers together, and all the variables

x^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}
$