8k^2-4=516

Solution for 8k^2-4=516 equation:

8k^2-4=516

We move all terms to the left:

8k^2-4-(516)=0

We add all the numbers together, and all the variables

8k^2-520=0

a = 8; b = 0; c = -520;
Δ = b2-4ac
Δ = 02-4·8·(-520)
Δ = 16640
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:

$\sqrt{\Delta}=\sqrt{16640}=\sqrt{256*65}=\sqrt{256}*\sqrt{65}=16\sqrt{65}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{65}}{2*8}=\frac{0-16\sqrt{65}}{16}
=-\frac{16\sqrt{65}}{16}
=-\sqrt{65}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{65}}{2*8}=\frac{0+16\sqrt{65}}{16}
=\frac{16\sqrt{65}}{16}
=\sqrt{65}
$