n2+19n+60=0

Solution for n2+19n+60=0 equation:

n2+19n+60=0

We add all the numbers together, and all the variables

n^2+19n+60=0

a = 1; b = 19; c = +60;
Δ = b2-4ac
Δ = 192-4·1·60
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*1}=\frac{-30}{2}
=-15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*1}=\frac{-8}{2}
=-4
$