6w^2-24w-12=0

Solution for 6w^2-24w-12=0 equation:

6w^2-24w-12=0

a = 6; b = -24; c = -12;
Δ = b2-4ac
Δ = -242-4·6·(-12)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*6}=\frac{24-12\sqrt{6}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*6}=\frac{24+12\sqrt{6}}{12}
$