w(w+56)=663

Solution for w(w+56)=663 equation:

w(w+56)=663

We move all terms to the left:

w(w+56)-(663)=0

We multiply parentheses

w^2+56w-663=0

a = 1; b = 56; c = -663;
Δ = b2-4ac
Δ = 562-4·1·(-663)
Δ = 5788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5788}=\sqrt{4*1447}=\sqrt{4}*\sqrt{1447}=2\sqrt{1447}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{1447}}{2*1}=\frac{-56-2\sqrt{1447}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{1447}}{2*1}=\frac{-56+2\sqrt{1447}}{2}
$