81y2-72y-15=0

Solution for 81y2-72y-15=0 equation:

81y^2-72y-15=0

a = 81; b = -72; c = -15;
Δ = b2-4ac
Δ = -722-4·81·(-15)
Δ = 10044
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:

$\sqrt{\Delta}=\sqrt{10044}=\sqrt{324*31}=\sqrt{324}*\sqrt{31}=18\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-18\sqrt{31}}{2*81}=\frac{72-18\sqrt{31}}{162}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+18\sqrt{31}}{2*81}=\frac{72+18\sqrt{31}}{162}
$