4w^2+100w=200

Solution for 4w^2+100w=200 equation:

4w^2+100w=200

We move all terms to the left:

4w^2+100w-(200)=0

a = 4; b = 100; c = -200;
Δ = b2-4ac
Δ = 1002-4·4·(-200)
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{33}}{2*4}=\frac{-100-20\sqrt{33}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{33}}{2*4}=\frac{-100+20\sqrt{33}}{8}
$