y^2-80y+1000=0

Solution for y^2-80y+1000=0 equation:

y^2-80y+1000=0

a = 1; b = -80; c = +1000;
Δ = b2-4ac
Δ = -802-4·1·1000
Δ = 2400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{6}}{2*1}=\frac{80-20\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{6}}{2*1}=\frac{80+20\sqrt{6}}{2}
$