x^2-80x+240=0

Solution for x^2-80x+240=0 equation:

x^2-80x+240=0

a = 1; b = -80; c = +240;
Δ = b2-4ac
Δ = -802-4·1·240
Δ = 5440
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:

$\sqrt{\Delta}=\sqrt{5440}=\sqrt{64*85}=\sqrt{64}*\sqrt{85}=8\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{85}}{2*1}=\frac{80-8\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{85}}{2*1}=\frac{80+8\sqrt{85}}{2}
$