4/9x2=3

Solution for 4/9x2=3 equation:

4/9x^2=3

We move all terms to the left:

4/9x^2-(3)=0


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

x^2!=0/9

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-3*9x^2+4=0

Wy multiply elements

-27x^2+4=0

a = -27; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-27)·4
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-27}=\frac{0-12\sqrt{3}}{-54}
=-\frac{12\sqrt{3}}{-54}
=-\frac{2\sqrt{3}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-27}=\frac{0+12\sqrt{3}}{-54}
=\frac{12\sqrt{3}}{-54}
=\frac{2\sqrt{3}}{-9}
$