8k^2-5=259

Solution for 8k^2-5=259 equation:

8k^2-5=259

We move all terms to the left:

8k^2-5-(259)=0

We add all the numbers together, and all the variables

8k^2-264=0

a = 8; b = 0; c = -264;
Δ = b2-4ac
Δ = 02-4·8·(-264)
Δ = 8448
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:

$\sqrt{\Delta}=\sqrt{8448}=\sqrt{256*33}=\sqrt{256}*\sqrt{33}=16\sqrt{33}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{33}}{2*8}=\frac{0-16\sqrt{33}}{16}
=-\frac{16\sqrt{33}}{16}
=-\sqrt{33}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{33}}{2*8}=\frac{0+16\sqrt{33}}{16}
=\frac{16\sqrt{33}}{16}
=\sqrt{33}
$