1/3x^2-44=0

Solution for 1/3x^2-44=0 equation:

1/3x^2-44=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-44*3x^2+1=0

Wy multiply elements

-132x^2+1=0

a = -132; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-132)·1
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*-132}=\frac{0-4\sqrt{33}}{-264}
=-\frac{4\sqrt{33}}{-264}
=-\frac{\sqrt{33}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*-132}=\frac{0+4\sqrt{33}}{-264}
=\frac{4\sqrt{33}}{-264}
=\frac{\sqrt{33}}{-66}
$