n2+13n+22=0

Solution for n2+13n+22=0 equation:

n2+13n+22=0

We add all the numbers together, and all the variables

n^2+13n+22=0

a = 1; b = 13; c = +22;
Δ = b2-4ac
Δ = 132-4·1·22
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-9}{2*1}=\frac{-22}{2}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+9}{2*1}=\frac{-4}{2}
=-2
$