108(x^2-3)=0

Solution for 108(x^2-3)=0 equation:

108(x^2-3)=0

We multiply parentheses

108x^2-324=0

a = 108; b = 0; c = -324;
Δ = b2-4ac
Δ = 02-4·108·(-324)
Δ = 139968
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:

$\sqrt{\Delta}=\sqrt{139968}=\sqrt{46656*3}=\sqrt{46656}*\sqrt{3}=216\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-216\sqrt{3}}{2*108}=\frac{0-216\sqrt{3}}{216}
=-\frac{216\sqrt{3}}{216}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+216\sqrt{3}}{2*108}=\frac{0+216\sqrt{3}}{216}
=\frac{216\sqrt{3}}{216}
=\sqrt{3}
$