2(y2-6y-9)=0

Solution for 2(y2-6y-9)=0 equation:

2(y2-6y-9)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

2y^2-12y-18=0

a = 2; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·2·(-18)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*2}=\frac{12-12\sqrt{2}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*2}=\frac{12+12\sqrt{2}}{4}
$