2w^2-8w-84=0

Solution for 2w^2-8w-84=0 equation:

2w^2-8w-84=0

a = 2; b = -8; c = -84;
Δ = b2-4ac
Δ = -82-4·2·(-84)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{46}}{2*2}=\frac{8-4\sqrt{46}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{46}}{2*2}=\frac{8+4\sqrt{46}}{4}
$