2y^2+6y+9=369

Solution for 2y^2+6y+9=369 equation:

2y^2+6y+9=369

We move all terms to the left:

2y^2+6y+9-(369)=0

We add all the numbers together, and all the variables

2y^2+6y-360=0

a = 2; b = 6; c = -360;
Δ = b2-4ac
Δ = 62-4·2·(-360)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-54}{2*2}=\frac{-60}{4}
=-15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+54}{2*2}=\frac{48}{4}
=12
$