1000=x^2+2x+2

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

1000=x^2+2x+2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-2x+998=0

a = -1; b = -2; c = +998;
Δ = b2-4ac
Δ = -22-4·(-1)·998
Δ = 3996
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:

$\sqrt{\Delta}=\sqrt{3996}=\sqrt{36*111}=\sqrt{36}*\sqrt{111}=6\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{111}}{2*-1}=\frac{2-6\sqrt{111}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{111}}{2*-1}=\frac{2+6\sqrt{111}}{-2}
$