4w^2-160w+425=0

Solution for 4w^2-160w+425=0 equation:

4w^2-160w+425=0

a = 4; b = -160; c = +425;
Δ = b2-4ac
Δ = -1602-4·4·425
Δ = 18800
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:

$\sqrt{\Delta}=\sqrt{18800}=\sqrt{400*47}=\sqrt{400}*\sqrt{47}=20\sqrt{47}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-20\sqrt{47}}{2*4}=\frac{160-20\sqrt{47}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+20\sqrt{47}}{2*4}=\frac{160+20\sqrt{47}}{8}
$