-3(3y+9)2y=-13

Solution for -3(3y+9)2y=-13 equation:

-3(3y+9)2y=-13

We move all terms to the left:

-3(3y+9)2y-(-13)=0

We add all the numbers together, and all the variables

-3(3y+9)2y+13=0

We multiply parentheses

-18y^2-54y+13=0

a = -18; b = -54; c = +13;
Δ = b2-4ac
Δ = -542-4·(-18)·13
Δ = 3852
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:

$\sqrt{\Delta}=\sqrt{3852}=\sqrt{36*107}=\sqrt{36}*\sqrt{107}=6\sqrt{107}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{107}}{2*-18}=\frac{54-6\sqrt{107}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{107}}{2*-18}=\frac{54+6\sqrt{107}}{-36}
$