2x^2=480^2

Solution for 2x^2=480^2 equation:

2x^2=480^2

We move all terms to the left:

2x^2-(480^2)=0

We add all the numbers together, and all the variables

2x^2-230400=0

a = 2; b = 0; c = -230400;
Δ = b2-4ac
Δ = 02-4·2·(-230400)
Δ = 1843200
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:

$\sqrt{\Delta}=\sqrt{1843200}=\sqrt{921600*2}=\sqrt{921600}*\sqrt{2}=960\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-960\sqrt{2}}{2*2}=\frac{0-960\sqrt{2}}{4}
=-\frac{960\sqrt{2}}{4}
=-240\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+960\sqrt{2}}{2*2}=\frac{0+960\sqrt{2}}{4}
=\frac{960\sqrt{2}}{4}
=240\sqrt{2}
$