w(2w+6)=328

Solution for w(2w+6)=328 equation:

w(2w+6)=328

We move all terms to the left:

w(2w+6)-(328)=0

We multiply parentheses

2w^2+6w-328=0

a = 2; b = 6; c = -328;
Δ = b2-4ac
Δ = 62-4·2·(-328)
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{665}}{2*2}=\frac{-6-2\sqrt{665}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{665}}{2*2}=\frac{-6+2\sqrt{665}}{4}
$