10000=2x*x

Solution for 10000=2x*x equation:

10000=2x*x

We move all terms to the left:

10000-(2x*x)=0

We add all the numbers together, and all the variables

-(+2x*x)+10000=0

We get rid of parentheses

-2x*x+10000=0

Wy multiply elements

-2x^2+10000=0

a = -2; b = 0; c = +10000;
Δ = b2-4ac
Δ = 02-4·(-2)·10000
Δ = 80000
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:

$\sqrt{\Delta}=\sqrt{80000}=\sqrt{40000*2}=\sqrt{40000}*\sqrt{2}=200\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{2}}{2*-2}=\frac{0-200\sqrt{2}}{-4}
=-\frac{200\sqrt{2}}{-4}
=-\frac{50\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{2}}{2*-2}=\frac{0+200\sqrt{2}}{-4}
=\frac{200\sqrt{2}}{-4}
=\frac{50\sqrt{2}}{-1}
$