X^2+56x+32=0

Solution for X^2+56x+32=0 equation:

X^2+56X+32=0

a = 1; b = 56; c = +32;
Δ = b2-4ac
Δ = 562-4·1·32
Δ = 3008
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:

$\sqrt{\Delta}=\sqrt{3008}=\sqrt{64*47}=\sqrt{64}*\sqrt{47}=8\sqrt{47}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{47}}{2*1}=\frac{-56-8\sqrt{47}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{47}}{2*1}=\frac{-56+8\sqrt{47}}{2}
$