0=2w^2+12w-144

Solution for 0=2w^2+12w-144 equation:

0=2w^2+12w-144

We move all terms to the left:

0-(2w^2+12w-144)=0

We add all the numbers together, and all the variables

-(2w^2+12w-144)=0

We get rid of parentheses

-2w^2-12w+144=0

a = -2; b = -12; c = +144;
Δ = b2-4ac
Δ = -122-4·(-2)·144
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*-2}=\frac{-24}{-4}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*-2}=\frac{48}{-4}
=-12
$