1/6x^2-81=0

Solution for 1/6x^2-81=0 equation:

1/6x^2-81=0


Domain of the equation: 6x^2!=0

x^2!=0/6

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-81*6x^2+1=0

Wy multiply elements

-486x^2+1=0

a = -486; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-486)·1
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{6}}{2*-486}=\frac{0-18\sqrt{6}}{-972}
=-\frac{18\sqrt{6}}{-972}
=-\frac{\sqrt{6}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{6}}{2*-486}=\frac{0+18\sqrt{6}}{-972}
=\frac{18\sqrt{6}}{-972}
=\frac{\sqrt{6}}{-54}
$