X^2+32x=-56

Solution for X^2+32x=-56 equation:

X^2+32X=-56

We move all terms to the left:

X^2+32X-(-56)=0

We add all the numbers together, and all the variables

X^2+32X+56=0

a = 1; b = 32; c = +56;
Δ = b2-4ac
Δ = 322-4·1·56
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-20\sqrt{2}}{2*1}=\frac{-32-20\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+20\sqrt{2}}{2*1}=\frac{-32+20\sqrt{2}}{2}
$