2w^2-100w-500=0

Solution for 2w^2-100w-500=0 equation:

2w^2-100w-500=0

a = 2; b = -100; c = -500;
Δ = b2-4ac
Δ = -1002-4·2·(-500)
Δ = 14000
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:

$\sqrt{\Delta}=\sqrt{14000}=\sqrt{400*35}=\sqrt{400}*\sqrt{35}=20\sqrt{35}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{35}}{2*2}=\frac{100-20\sqrt{35}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{35}}{2*2}=\frac{100+20\sqrt{35}}{4}
$