$3x^2-108=0$

Step 1 ：We are given the quadratic equation $3x^2-108=0$.

Step 2 ：This is a quadratic equation in the form of $a{x}^2+bx+c=0$. 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 $D=b^2-4ac=0^2-4\ast 3\ast (-108)=1296$.

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

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 $\boxed{{\displaystyle x=6.0}}$ and $\boxed{{\displaystyle x=-6.0}}$.