2w^2+6w-96=0

Solution for 2w^2+6w-96=0 equation:

2w^2+6w-96=0

a = 2; b = 6; c = -96;
Δ = b2-4ac
Δ = 62-4·2·(-96)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{201}}{2*2}=\frac{-6-2\sqrt{201}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{201}}{2*2}=\frac{-6+2\sqrt{201}}{4}
$