11.5^2=2x^2

Solution for 11.5^2=2x^2 equation:

11.5^2=2x^2

We move all terms to the left:

11.5^2-(2x^2)=0

We add all the numbers together, and all the variables

-2x^2+132.25=0

a = -2; b = 0; c = +132.25;
Δ = b2-4ac
Δ = 02-4·(-2)·132.25
Δ = 1058
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:

$\sqrt{\Delta}=\sqrt{1058}=\sqrt{529*2}=\sqrt{529}*\sqrt{2}=23\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-23\sqrt{2}}{2*-2}=\frac{0-23\sqrt{2}}{-4}
=-\frac{23\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+23\sqrt{2}}{2*-2}=\frac{0+23\sqrt{2}}{-4}
=\frac{23\sqrt{2}}{-4}
$