(3125)^2=2x^2

Solution for (3125)^2=2x^2 equation:

(3125)^2=2x^2

We move all terms to the left:

(3125)^2-(2x^2)=0

We add all the numbers together, and all the variables

-2x^2+9765625=0

a = -2; b = 0; c = +9765625;
Δ = b2-4ac
Δ = 02-4·(-2)·9765625
Δ = 78125000
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:

$\sqrt{\Delta}=\sqrt{78125000}=\sqrt{39062500*2}=\sqrt{39062500}*\sqrt{2}=6250\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6250\sqrt{2}}{2*-2}=\frac{0-6250\sqrt{2}}{-4}
=-\frac{6250\sqrt{2}}{-4}
=-\frac{3125\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6250\sqrt{2}}{2*-2}=\frac{0+6250\sqrt{2}}{-4}
=\frac{6250\sqrt{2}}{-4}
=\frac{3125\sqrt{2}}{-2}
$