(2x)2=4/9

Solution for (2x)2=4/9 equation:

(2x)2=4/9

We move all terms to the left:

(2x)2-(4/9)=0

We add all the numbers together, and all the variables

2x2-(+4/9)=0

We add all the numbers together, and all the variables

2x^2-(+4/9)=0

We get rid of parentheses

2x^2-4/9=0

We multiply all the terms by the denominator


2x^2*9-4=0

Wy multiply elements

18x^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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{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}
$
$x_{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}
$