$3 x^{2}-108=0$

Step 1 ：We are given the quadratic equation \(3x^{2} - 108 = 0\).

Step 2 ：This is a quadratic equation in the form of \(ax^{2} + bx + c = 0\). The general solution to such an equation is given by the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\).

Step 3 ：In this case, \(a = 3\), \(b = 0\), and \(c = -108\). We can substitute these values into the quadratic formula to find the solutions for \(x\).

Step 4 ：Calculate the discriminant \(D = b^{2} - 4ac = 0^{2} - 4*3*(-108) = 1296\).

Step 5 ：Substitute \(a\), \(b\), and \(D\) into the quadratic formula, we get \(x1 = \frac{-0 + \sqrt{1296}}{2*3} = 6.0\) and \(x2 = \frac{-0 - \sqrt{1296}}{2*3} = -6.0\).

Step 6 ：The solutions to the equation are \(x = 6.0\) and \(x = -6.0\). These are the values of \(x\) that satisfy the equation \(3x^{2} - 108 = 0\).

Step 7 ：Final Answer: The solutions to the equation are \(\boxed{x = 6.0}\) and \(\boxed{x = -6.0}\).