2(30-y)2y=216

Solution for 2(30-y)2y=216 equation:

2(30-y)2y=216

We move all terms to the left:

2(30-y)2y-(216)=0

We add all the numbers together, and all the variables

2(-1y+30)2y-216=0

We multiply parentheses

-4y^2+120y-216=0

a = -4; b = 120; c = -216;
Δ = b2-4ac
Δ = 1202-4·(-4)·(-216)
Δ = 10944
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:

$\sqrt{\Delta}=\sqrt{10944}=\sqrt{576*19}=\sqrt{576}*\sqrt{19}=24\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{19}}{2*-4}=\frac{-120-24\sqrt{19}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{19}}{2*-4}=\frac{-120+24\sqrt{19}}{-8}
$