w2=8116

Solution for w2=8116 equation:

w2=8116

We move all terms to the left:

w2-(8116)=0

We add all the numbers together, and all the variables

w^2-8116=0

a = 1; b = 0; c = -8116;
Δ = b2-4ac
Δ = 02-4·1·(-8116)
Δ = 32464
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:

$\sqrt{\Delta}=\sqrt{32464}=\sqrt{16*2029}=\sqrt{16}*\sqrt{2029}=4\sqrt{2029}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2029}}{2*1}=\frac{0-4\sqrt{2029}}{2}
=-\frac{4\sqrt{2029}}{2}
=-2\sqrt{2029}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2029}}{2*1}=\frac{0+4\sqrt{2029}}{2}
=\frac{4\sqrt{2029}}{2}
=2\sqrt{2029}
$