x^2-12x-589=0

Solution for x^2-12x-589=0 equation:

x^2-12x-589=0

a = 1; b = -12; c = -589;
Δ = b2-4ac
Δ = -122-4·1·(-589)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-50}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+50}{2*1}=\frac{62}{2}
=31
$