4w^2-8w=404

Solution for 4w^2-8w=404 equation:

4w^2-8w=404

We move all terms to the left:

4w^2-8w-(404)=0

a = 4; b = -8; c = -404;
Δ = b2-4ac
Δ = -82-4·4·(-404)
Δ = 6528
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:

$\sqrt{\Delta}=\sqrt{6528}=\sqrt{64*102}=\sqrt{64}*\sqrt{102}=8\sqrt{102}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{102}}{2*4}=\frac{8-8\sqrt{102}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{102}}{2*4}=\frac{8+8\sqrt{102}}{8}
$