1000=1r^2

Solution for 1000=1r^2 equation:

1000=1r^2

We move all terms to the left:

1000-(1r^2)=0

a = -1; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-1)·1000
Δ = 4000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*-1}=\frac{0-20\sqrt{10}}{-2}
=-\frac{20\sqrt{10}}{-2}
=-\frac{10\sqrt{10}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*-1}=\frac{0+20\sqrt{10}}{-2}
=\frac{20\sqrt{10}}{-2}
=\frac{10\sqrt{10}}{-1}
$