k^2-6k-19=-4

Solution for k^2-6k-19=-4 equation:

k^2-6k-19=-4

We move all terms to the left:

k^2-6k-19-(-4)=0

We add all the numbers together, and all the variables

k^2-6k-15=0

a = 1; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·1·(-15)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*1}=\frac{6-4\sqrt{6}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*1}=\frac{6+4\sqrt{6}}{2}
$