100^2=3.14r^2

Solution for 100^2=3.14r^2 equation:

100^2=3.14r^2

We move all terms to the left:

100^2-(3.14r^2)=0

We add all the numbers together, and all the variables

-(3.14r^2)+10000=0

We get rid of parentheses

-3.14r^2+10000=0

a = -3.14; b = 0; c = +10000;
Δ = b2-4ac
Δ = 02-4·(-3.14)·10000
Δ = 125600
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:

$\sqrt{\Delta}=\sqrt{125600}=\sqrt{400*314}=\sqrt{400}*\sqrt{314}=20\sqrt{314}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{314}}{2*-3.14}=\frac{0-20\sqrt{314}}{-6.28}
=-\frac{20\sqrt{314}}{-6.28}
=-\frac{10\sqrt{314}}{-3.14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{314}}{2*-3.14}=\frac{0+20\sqrt{314}}{-6.28}
=\frac{20\sqrt{314}}{-6.28}
=\frac{10\sqrt{314}}{-3.14}
$