2(27-6y)6y=24

Solution for 2(27-6y)6y=24 equation:

2(27-6y)6y=24

We move all terms to the left:

2(27-6y)6y-(24)=0

We add all the numbers together, and all the variables

2(-6y+27)6y-24=0

We multiply parentheses

-72y^2+324y-24=0

a = -72; b = 324; c = -24;
Δ = b2-4ac
Δ = 3242-4·(-72)·(-24)
Δ = 98064
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:

$\sqrt{\Delta}=\sqrt{98064}=\sqrt{144*681}=\sqrt{144}*\sqrt{681}=12\sqrt{681}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-12\sqrt{681}}{2*-72}=\frac{-324-12\sqrt{681}}{-144}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+12\sqrt{681}}{2*-72}=\frac{-324+12\sqrt{681}}{-144}
$