1/x^2-6=0

Solution for 1/x^2-6=0 equation:

1/x^2-6=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-6*x^2+1=0

We add all the numbers together, and all the variables

-6x^2+1=0

a = -6; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-6)·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-6}=\frac{0-2\sqrt{6}}{-12}
=-\frac{2\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-6}=\frac{0+2\sqrt{6}}{-12}
=\frac{2\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-6}
$