(3y+27)y=-6

Solution for (3y+27)y=-6 equation:

(3y+27)y=-6

We move all terms to the left:

(3y+27)y-(-6)=0

We add all the numbers together, and all the variables

(3y+27)y+6=0

We multiply parentheses

3y^2+27y+6=0

a = 3; b = 27; c = +6;
Δ = b2-4ac
Δ = 272-4·3·6
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{73}}{2*3}=\frac{-27-3\sqrt{73}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{73}}{2*3}=\frac{-27+3\sqrt{73}}{6}
$