2w(w+6)=228

Solution for 2w(w+6)=228 equation:

2w(w+6)=228

We move all terms to the left:

2w(w+6)-(228)=0

We multiply parentheses

2w^2+12w-228=0

a = 2; b = 12; c = -228;
Δ = b2-4ac
Δ = 122-4·2·(-228)
Δ = 1968
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:

$\sqrt{\Delta}=\sqrt{1968}=\sqrt{16*123}=\sqrt{16}*\sqrt{123}=4\sqrt{123}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{123}}{2*2}=\frac{-12-4\sqrt{123}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{123}}{2*2}=\frac{-12+4\sqrt{123}}{4}
$