k^2-12k+7=-2

Solution for k^2-12k+7=-2 equation:

k^2-12k+7=-2

We move all terms to the left:

k^2-12k+7-(-2)=0

We add all the numbers together, and all the variables

k^2-12k+9=0

a = 1; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·1·9
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3}}{2*1}=\frac{12-6\sqrt{3}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3}}{2*1}=\frac{12+6\sqrt{3}}{2}
$