2(y^2+3y)=9

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

2(y^2+3y)=9

We move all terms to the left:

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

We multiply parentheses

2y^2+6y-9=0

a = 2; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·2·(-9)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*2}=\frac{-6-6\sqrt{3}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*2}=\frac{-6+6\sqrt{3}}{4}
$