80w2=50

Solution for 80w2=50 equation:

80w^2=50

We move all terms to the left:

80w^2-(50)=0

a = 80; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·80·(-50)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*80}=\frac{0-40\sqrt{10}}{160}
=-\frac{40\sqrt{10}}{160}
=-\frac{\sqrt{10}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*80}=\frac{0+40\sqrt{10}}{160}
=\frac{40\sqrt{10}}{160}
=\frac{\sqrt{10}}{4}
$