k^2-4k^2+1=-5

Solution for k^2-4k^2+1=-5 equation:

k^2-4k^2+1=-5

We move all terms to the left:

k^2-4k^2+1-(-5)=0

We add all the numbers together, and all the variables

-3k^2+6=0

a = -3; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-3)·6
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-3}=\frac{0-6\sqrt{2}}{-6}
=-\frac{6\sqrt{2}}{-6}
=-\frac{\sqrt{2}}{-1}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-3}=\frac{0+6\sqrt{2}}{-6}
=\frac{6\sqrt{2}}{-6}
=\frac{\sqrt{2}}{-1}
$