300^2=3r^2

Solution for 300^2=3r^2 equation:

300^2=3r^2

We move all terms to the left:

300^2-(3r^2)=0

We add all the numbers together, and all the variables

-3r^2+90000=0

a = -3; b = 0; c = +90000;
Δ = b2-4ac
Δ = 02-4·(-3)·90000
Δ = 1080000
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:

$\sqrt{\Delta}=\sqrt{1080000}=\sqrt{360000*3}=\sqrt{360000}*\sqrt{3}=600\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{3}}{2*-3}=\frac{0-600\sqrt{3}}{-6}
=-\frac{600\sqrt{3}}{-6}
=-\frac{100\sqrt{3}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{3}}{2*-3}=\frac{0+600\sqrt{3}}{-6}
=\frac{600\sqrt{3}}{-6}
=\frac{100\sqrt{3}}{-1}
$