2(3y+24)9y=27

Solution for 2(3y+24)9y=27 equation:

2(3y+24)9y=27

We move all terms to the left:

2(3y+24)9y-(27)=0

We multiply parentheses

54y^2+432y-27=0

a = 54; b = 432; c = -27;
Δ = b2-4ac
Δ = 4322-4·54·(-27)
Δ = 192456
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:

$\sqrt{\Delta}=\sqrt{192456}=\sqrt{2916*66}=\sqrt{2916}*\sqrt{66}=54\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(432)-54\sqrt{66}}{2*54}=\frac{-432-54\sqrt{66}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(432)+54\sqrt{66}}{2*54}=\frac{-432+54\sqrt{66}}{108}
$