2w(2)+2w=96

Solution for 2w(2)+2w=96 equation:

2w(2)+2w=96

We move all terms to the left:

2w(2)+2w-(96)=0

We add all the numbers together, and all the variables

2w^2+2w-96=0

a = 2; b = 2; c = -96;
Δ = b2-4ac
Δ = 22-4·2·(-96)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{193}}{2*2}=\frac{-2-2\sqrt{193}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{193}}{2*2}=\frac{-2+2\sqrt{193}}{4}
$