30y^2+108y+81=0

Solution for 30y^2+108y+81=0 equation:

30y^2+108y+81=0

a = 30; b = 108; c = +81;
Δ = b2-4ac
Δ = 1082-4·30·81
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-18\sqrt{6}}{2*30}=\frac{-108-18\sqrt{6}}{60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+18\sqrt{6}}{2*30}=\frac{-108+18\sqrt{6}}{60}
$