k^2+15k+5=-6

Solution for k^2+15k+5=-6 equation:

k^2+15k+5=-6

We move all terms to the left:

k^2+15k+5-(-6)=0

We add all the numbers together, and all the variables

k^2+15k+11=0

a = 1; b = 15; c = +11;
Δ = b2-4ac
Δ = 152-4·1·11
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{181}}{2*1}=\frac{-15-\sqrt{181}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{181}}{2*1}=\frac{-15+\sqrt{181}}{2}
$