2x^2=500^2

Solution for 2x^2=500^2 equation:

2x^2=500^2

We move all terms to the left:

2x^2-(500^2)=0

We add all the numbers together, and all the variables

2x^2-250000=0

a = 2; b = 0; c = -250000;
Δ = b2-4ac
Δ = 02-4·2·(-250000)
Δ = 2000000
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:

$\sqrt{\Delta}=\sqrt{2000000}=\sqrt{1000000*2}=\sqrt{1000000}*\sqrt{2}=1000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{2}}{2*2}=\frac{0-1000\sqrt{2}}{4}
=-\frac{1000\sqrt{2}}{4}
=-250\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{2}}{2*2}=\frac{0+1000\sqrt{2}}{4}
=\frac{1000\sqrt{2}}{4}
=250\sqrt{2}
$