k^2-4k-46=-6

Solution for k^2-4k-46=-6 equation:

k^2-4k-46=-6

We move all terms to the left:

k^2-4k-46-(-6)=0

We add all the numbers together, and all the variables

k^2-4k-40=0

a = 1; b = -4; c = -40;
Δ = b2-4ac
Δ = -42-4·1·(-40)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*1}=\frac{4-4\sqrt{11}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*1}=\frac{4+4\sqrt{11}}{2}
$