w2+w-208=0

Solution for w2+w-208=0 equation:

w2+w-208=0

We add all the numbers together, and all the variables

w^2+w-208=0

a = 1; b = 1; c = -208;
Δ = b2-4ac
Δ = 12-4·1·(-208)
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{17}}{2*1}=\frac{-1-7\sqrt{17}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{17}}{2*1}=\frac{-1+7\sqrt{17}}{2}
$