x^2=1000-2x

Solution for x^2=1000-2x equation:

x^2=1000-2x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2+2x-1000=0

a = 1; b = 2; c = -1000;
Δ = b2-4ac
Δ = 22-4·1·(-1000)
Δ = 4004
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:

$\sqrt{\Delta}=\sqrt{4004}=\sqrt{4*1001}=\sqrt{4}*\sqrt{1001}=2\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1001}}{2*1}=\frac{-2-2\sqrt{1001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1001}}{2*1}=\frac{-2+2\sqrt{1001}}{2}
$