81r^2-6=19

Solution for 81r^2-6=19 equation:

81r^2-6=19

We move all terms to the left:

81r^2-6-(19)=0

We add all the numbers together, and all the variables

81r^2-25=0

a = 81; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·81·(-25)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*81}=\frac{-90}{162}
=-5/9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*81}=\frac{90}{162}
=5/9
$