2(9y-6)8y=18

Solution for 2(9y-6)8y=18 equation:

2(9y-6)8y=18

We move all terms to the left:

2(9y-6)8y-(18)=0

We multiply parentheses

144y^2-96y-18=0

a = 144; b = -96; c = -18;
Δ = b2-4ac
Δ = -962-4·144·(-18)
Δ = 19584
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:

$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-24\sqrt{34}}{2*144}=\frac{96-24\sqrt{34}}{288}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+24\sqrt{34}}{2*144}=\frac{96+24\sqrt{34}}{288}
$