w(w+6)=96

Solution for w(w+6)=96 equation:

w(w+6)=96

We move all terms to the left:

w(w+6)-(96)=0

We multiply parentheses

w^2+6w-96=0

a = 1; b = 6; c = -96;
Δ = b2-4ac
Δ = 62-4·1·(-96)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{105}}{2*1}=\frac{-6-2\sqrt{105}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{105}}{2*1}=\frac{-6+2\sqrt{105}}{2}
$