(-2w^2)-12w-9=0

Solution for (-2w^2)-12w-9=0 equation:

(-2w^2)-12w-9=0

We get rid of parentheses

-2w^2-12w-9=0

a = -2; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·(-2)·(-9)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*-2}=\frac{12-6\sqrt{2}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*-2}=\frac{12+6\sqrt{2}}{-4}
$