w(2w+6)=288

Solution for w(2w+6)=288 equation:

w(2w+6)=288

We move all terms to the left:

w(2w+6)-(288)=0

We multiply parentheses

2w^2+6w-288=0

a = 2; b = 6; c = -288;
Δ = b2-4ac
Δ = 62-4·2·(-288)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{65}}{2*2}=\frac{-6-6\sqrt{65}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{65}}{2*2}=\frac{-6+6\sqrt{65}}{4}
$