2=1/9x^2-2

Solution for 2=1/9x^2-2 equation:

2=1/9x^2-2

We move all terms to the left:

2-(1/9x^2-2)=0


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

x∈R


We get rid of parentheses

-1/9x^2+2+2=0

We multiply all the terms by the denominator


2*9x^2+2*9x^2-1=0

Wy multiply elements

18x^2+18x^2-1=0

We add all the numbers together, and all the variables

36x^2-1=0

a = 36; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·36·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*36}=\frac{-12}{72}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*36}=\frac{12}{72}
=1/6
$