3(3y^2+9y+9)=378

Solution for 3(3y^2+9y+9)=378 equation:

3(3y^2+9y+9)=378

We move all terms to the left:

3(3y^2+9y+9)-(378)=0

We multiply parentheses

9y^2+27y+27-378=0

We add all the numbers together, and all the variables

9y^2+27y-351=0

a = 9; b = 27; c = -351;
Δ = b2-4ac
Δ = 272-4·9·(-351)
Δ = 13365
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:

$\sqrt{\Delta}=\sqrt{13365}=\sqrt{81*165}=\sqrt{81}*\sqrt{165}=9\sqrt{165}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9\sqrt{165}}{2*9}=\frac{-27-9\sqrt{165}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9\sqrt{165}}{2*9}=\frac{-27+9\sqrt{165}}{18}
$