r^2+225=81r^2

Solution for r^2+225=81r^2 equation:

r^2+225=81r^2

We move all terms to the left:

r^2+225-(81r^2)=0

We add all the numbers together, and all the variables

-80r^2+225=0

a = -80; b = 0; c = +225;
Δ = b2-4ac
Δ = 02-4·(-80)·225
Δ = 72000
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:

$\sqrt{\Delta}=\sqrt{72000}=\sqrt{14400*5}=\sqrt{14400}*\sqrt{5}=120\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{5}}{2*-80}=\frac{0-120\sqrt{5}}{-160}
=-\frac{120\sqrt{5}}{-160}
=-\frac{3\sqrt{5}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{5}}{2*-80}=\frac{0+120\sqrt{5}}{-160}
=\frac{120\sqrt{5}}{-160}
=\frac{3\sqrt{5}}{-4}
$