2(9k^2-2)=0

Solution for 2(9k^2-2)=0 equation:

2(9k^2-2)=0

We multiply parentheses

18k^2-4=0

a = 18; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·18·(-4)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*18}=\frac{0-12\sqrt{2}}{36}
=-\frac{12\sqrt{2}}{36}
=-\frac{\sqrt{2}}{3}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*18}=\frac{0+12\sqrt{2}}{36}
=\frac{12\sqrt{2}}{36}
=\frac{\sqrt{2}}{3}
$