n^2+40n+60=0

Solution for n^2+40n+60=0 equation:

n^2+40n+60=0

a = 1; b = 40; c = +60;
Δ = b2-4ac
Δ = 402-4·1·60
Δ = 1360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{85}}{2*1}=\frac{-40-4\sqrt{85}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{85}}{2*1}=\frac{-40+4\sqrt{85}}{2}
$