x^2-586x+2880=0

Solution for x^2-586x+2880=0 equation:

x^2-586x+2880=0

a = 1; b = -586; c = +2880;
Δ = b2-4ac
Δ = -5862-4·1·2880
Δ = 331876
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:

$\sqrt{\Delta}=\sqrt{331876}=\sqrt{4*82969}=\sqrt{4}*\sqrt{82969}=2\sqrt{82969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-586)-2\sqrt{82969}}{2*1}=\frac{586-2\sqrt{82969}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-586)+2\sqrt{82969}}{2*1}=\frac{586+2\sqrt{82969}}{2}
$