2y(6+y)=36

Solution for 2y(6+y)=36 equation:

2y(6+y)=36

We move all terms to the left:

2y(6+y)-(36)=0

We add all the numbers together, and all the variables

2y(y+6)-36=0

We multiply parentheses

2y^2+12y-36=0

a = 2; b = 12; c = -36;
Δ = b2-4ac
Δ = 122-4·2·(-36)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{3}}{2*2}=\frac{-12-12\sqrt{3}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{3}}{2*2}=\frac{-12+12\sqrt{3}}{4}
$