(6+3y)(6-3y)=2

Solution for (6+3y)(6-3y)=2 equation:

(6+3y)(6-3y)=2

We move all terms to the left:

(6+3y)(6-3y)-(2)=0

We add all the numbers together, and all the variables

(3y+6)(-3y+6)-2=0

We multiply parentheses ..

(-9y^2+18y-18y+36)-2=0

We get rid of parentheses

-9y^2+18y-18y+36-2=0

We add all the numbers together, and all the variables

-9y^2+34=0

a = -9; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-9)·34
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{34}}{2*-9}=\frac{0-6\sqrt{34}}{-18}
=-\frac{6\sqrt{34}}{-18}
=-\frac{\sqrt{34}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{34}}{2*-9}=\frac{0+6\sqrt{34}}{-18}
=\frac{6\sqrt{34}}{-18}
=\frac{\sqrt{34}}{-3}
$