1000^2=10x*x

Solution for 1000^2=10x*x equation:

1000^2=10x*x

We move all terms to the left:

1000^2-(10x*x)=0

We add all the numbers together, and all the variables

-(+10x*x)+1000^2=0

We add all the numbers together, and all the variables

-(+10x*x)+1000000=0

We get rid of parentheses

-10x*x+1000000=0

Wy multiply elements

-10x^2+1000000=0

a = -10; b = 0; c = +1000000;
Δ = b2-4ac
Δ = 02-4·(-10)·1000000
Δ = 40000000
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:

$\sqrt{\Delta}=\sqrt{40000000}=\sqrt{4000000*10}=\sqrt{4000000}*\sqrt{10}=2000\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{10}}{2*-10}=\frac{0-2000\sqrt{10}}{-20}
=-\frac{2000\sqrt{10}}{-20}
=-\frac{100\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{10}}{2*-10}=\frac{0+2000\sqrt{10}}{-20}
=\frac{2000\sqrt{10}}{-20}
=\frac{100\sqrt{10}}{-1}
$