w^2+2w-2=120

Solution for w^2+2w-2=120 equation:

w^2+2w-2=120

We move all terms to the left:

w^2+2w-2-(120)=0

We add all the numbers together, and all the variables

w^2+2w-122=0

a = 1; b = 2; c = -122;
Δ = b2-4ac
Δ = 22-4·1·(-122)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{123}}{2*1}=\frac{-2-2\sqrt{123}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{123}}{2*1}=\frac{-2+2\sqrt{123}}{2}
$