k^2+20k+84=-15

Solution for k^2+20k+84=-15 equation:

k^2+20k+84=-15

We move all terms to the left:

k^2+20k+84-(-15)=0

We add all the numbers together, and all the variables

k^2+20k+99=0

a = 1; b = 20; c = +99;
Δ = b2-4ac
Δ = 202-4·1·99
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2}{2*1}=\frac{-22}{2}
=-11
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2}{2*1}=\frac{-18}{2}
=-9
$