18w^2-24w-8=0

Solution for 18w^2-24w-8=0 equation:

18w^2-24w-8=0

a = 18; b = -24; c = -8;
Δ = b2-4ac
Δ = -242-4·18·(-8)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*18}=\frac{24-24\sqrt{2}}{36}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*18}=\frac{24+24\sqrt{2}}{36}
$