x^2-80x+550=0

Solution for x^2-80x+550=0 equation:

x^2-80x+550=0

a = 1; b = -80; c = +550;
Δ = b2-4ac
Δ = -802-4·1·550
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-10\sqrt{42}}{2*1}=\frac{80-10\sqrt{42}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+10\sqrt{42}}{2*1}=\frac{80+10\sqrt{42}}{2}
$