2x^2=400^2

Solution for 2x^2=400^2 equation:

2x^2=400^2

We move all terms to the left:

2x^2-(400^2)=0

We add all the numbers together, and all the variables

2x^2-160000=0

a = 2; b = 0; c = -160000;
Δ = b2-4ac
Δ = 02-4·2·(-160000)
Δ = 1280000
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:

$\sqrt{\Delta}=\sqrt{1280000}=\sqrt{640000*2}=\sqrt{640000}*\sqrt{2}=800\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{2}}{2*2}=\frac{0-800\sqrt{2}}{4}
=-\frac{800\sqrt{2}}{4}
=-200\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{2}}{2*2}=\frac{0+800\sqrt{2}}{4}
=\frac{800\sqrt{2}}{4}
=200\sqrt{2}
$