108x^2=128

Solution for 108x^2=128 equation:

108x^2=128

We move all terms to the left:

108x^2-(128)=0

a = 108; b = 0; c = -128;
Δ = b2-4ac
Δ = 02-4·108·(-128)
Δ = 55296
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:

$\sqrt{\Delta}=\sqrt{55296}=\sqrt{9216*6}=\sqrt{9216}*\sqrt{6}=96\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{6}}{2*108}=\frac{0-96\sqrt{6}}{216}
=-\frac{96\sqrt{6}}{216}
=-\frac{4\sqrt{6}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{6}}{2*108}=\frac{0+96\sqrt{6}}{216}
=\frac{96\sqrt{6}}{216}
=\frac{4\sqrt{6}}{9}
$