780^2=2(x^2)

Solution for 780^2=2(x^2) equation:

780^2=2(x^2)

We move all terms to the left:

780^2-(2(x^2))=0

determiningTheFunctionDomain
-2x^2+780^2=0

We add all the numbers together, and all the variables

-2x^2+608400=0

a = -2; b = 0; c = +608400;
Δ = b2-4ac
Δ = 02-4·(-2)·608400
Δ = 4867200
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:

$\sqrt{\Delta}=\sqrt{4867200}=\sqrt{2433600*2}=\sqrt{2433600}*\sqrt{2}=1560\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1560\sqrt{2}}{2*-2}=\frac{0-1560\sqrt{2}}{-4}
=-\frac{1560\sqrt{2}}{-4}
=-\frac{390\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1560\sqrt{2}}{2*-2}=\frac{0+1560\sqrt{2}}{-4}
=\frac{1560\sqrt{2}}{-4}
=\frac{390\sqrt{2}}{-1}
$