k^2+16k+61=6

Solution for k^2+16k+61=6 equation:

k^2+16k+61=6

We move all terms to the left:

k^2+16k+61-(6)=0

We add all the numbers together, and all the variables

k^2+16k+55=0

a = 1; b = 16; c = +55;
Δ = b2-4ac
Δ = 162-4·1·55
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-6}{2*1}=\frac{-22}{2}
=-11
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+6}{2*1}=\frac{-10}{2}
=-5
$