k^2=-6-7k

Solution for k^2=-6-7k equation:

k^2=-6-7k

We move all terms to the left:

k^2-(-6-7k)=0

We add all the numbers together, and all the variables

k^2-(-7k-6)=0

We get rid of parentheses

k^2+7k+6=0

a = 1; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*1}=\frac{-12}{2}
=-6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*1}=\frac{-2}{2}
=-1
$