x^2+162x+585=0

Solution for x^2+162x+585=0 equation:

x^2+162x+585=0

a = 1; b = 162; c = +585;
Δ = b2-4ac
Δ = 1622-4·1·585
Δ = 23904
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:

$\sqrt{\Delta}=\sqrt{23904}=\sqrt{144*166}=\sqrt{144}*\sqrt{166}=12\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-12\sqrt{166}}{2*1}=\frac{-162-12\sqrt{166}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+12\sqrt{166}}{2*1}=\frac{-162+12\sqrt{166}}{2}
$