4/9k2=2

Solution for 4/9k2=2 equation:

4/9k^2=2

We move all terms to the left:

4/9k^2-(2)=0


Domain of the equation: 9k^2!=0

k^2!=0/9

k^2!=√0

k!=0

k∈R


We multiply all the terms by the denominator


-2*9k^2+4=0

Wy multiply elements

-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}
$