81r^2-3=0

Solution for 81r^2-3=0 equation:

81r^2-3=0

a = 81; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·81·(-3)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*81}=\frac{0-18\sqrt{3}}{162}
=-\frac{18\sqrt{3}}{162}
=-\frac{\sqrt{3}}{9}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*81}=\frac{0+18\sqrt{3}}{162}
=\frac{18\sqrt{3}}{162}
=\frac{\sqrt{3}}{9}
$