x^2-80x+100=0

Solution for x^2-80x+100=0 equation:

x^2-80x+100=0

a = 1; b = -80; c = +100;
Δ = b2-4ac
Δ = -802-4·1·100
Δ = 6000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{15}}{2*1}=\frac{80-20\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{15}}{2*1}=\frac{80+20\sqrt{15}}{2}
$