8k^2-13=0

Solution for 8k^2-13=0 equation:

8k^2-13=0

a = 8; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·8·(-13)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*8}=\frac{0-4\sqrt{26}}{16}
=-\frac{4\sqrt{26}}{16}
=-\frac{\sqrt{26}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*8}=\frac{0+4\sqrt{26}}{16}
=\frac{4\sqrt{26}}{16}
=\frac{\sqrt{26}}{4}
$