1/6x^2-16=0

Solution for 1/6x^2-16=0 equation:

1/6x^2-16=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


-16*6x^2+1=0

Wy multiply elements

-96x^2+1=0

a = -96; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-96)·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-96}=\frac{0-8\sqrt{6}}{-192}
=-\frac{8\sqrt{6}}{-192}
=-\frac{\sqrt{6}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-96}=\frac{0+8\sqrt{6}}{-192}
=\frac{8\sqrt{6}}{-192}
=\frac{\sqrt{6}}{-24}
$