81y^2-9y-1=0

Solution for 81y^2-9y-1=0 equation:

81y^2-9y-1=0

a = 81; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·81·(-1)
Δ = 405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{5}}{2*81}=\frac{9-9\sqrt{5}}{162}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{5}}{2*81}=\frac{9+9\sqrt{5}}{162}
$