4k^2=18

Solution for 4k^2=18 equation:

4k^2=18

We move all terms to the left:

4k^2-(18)=0

a = 4; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·4·(-18)
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*4}=\frac{0-12\sqrt{2}}{8}
=-\frac{12\sqrt{2}}{8}
=-\frac{3\sqrt{2}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*4}=\frac{0+12\sqrt{2}}{8}
=\frac{12\sqrt{2}}{8}
=\frac{3\sqrt{2}}{2}
$