108=2x^2

Solution for 108=2x^2 equation:

108=2x^2

We move all terms to the left:

108-(2x^2)=0

a = -2; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-2)·108
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*-2}=\frac{0-12\sqrt{6}}{-4}
=-\frac{12\sqrt{6}}{-4}
=-\frac{3\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*-2}=\frac{0+12\sqrt{6}}{-4}
=\frac{12\sqrt{6}}{-4}
=\frac{3\sqrt{6}}{-1}
$