234*234=2x^2

Solution for 234*234=2x^2 equation:

234*234=2x^2

We move all terms to the left:

234*234-(2x^2)=0

We add all the numbers together, and all the variables

-2x^2+54756=0

a = -2; b = 0; c = +54756;
Δ = b2-4ac
Δ = 02-4·(-2)·54756
Δ = 438048
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:

$\sqrt{\Delta}=\sqrt{438048}=\sqrt{219024*2}=\sqrt{219024}*\sqrt{2}=468\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-468\sqrt{2}}{2*-2}=\frac{0-468\sqrt{2}}{-4}
=-\frac{468\sqrt{2}}{-4}
=-\frac{117\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+468\sqrt{2}}{2*-2}=\frac{0+468\sqrt{2}}{-4}
=\frac{468\sqrt{2}}{-4}
=\frac{117\sqrt{2}}{-1}
$