1000=3.14r^2

Solution for 1000=3.14r^2 equation:

1000=3.14r^2

We move all terms to the left:

1000-(3.14r^2)=0

We get rid of parentheses

-3.14r^2+1000=0

a = -3.14; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-3.14)·1000
Δ = 12560
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:

$\sqrt{\Delta}=\sqrt{12560}=\sqrt{16*785}=\sqrt{16}*\sqrt{785}=4\sqrt{785}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{785}}{2*-3.14}=\frac{0-4\sqrt{785}}{-6.28}
=-\frac{4\sqrt{785}}{-6.28}
=-\frac{2\sqrt{785}}{-3.14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{785}}{2*-3.14}=\frac{0+4\sqrt{785}}{-6.28}
=\frac{4\sqrt{785}}{-6.28}
=\frac{2\sqrt{785}}{-3.14}
$