2y+18=12-6y(y+7)

Solution for 2y+18=12-6y(y+7) equation:

2y+18=12-6y(y+7)

We move all terms to the left:

2y+18-(12-6y(y+7))=0


We calculate terms in parentheses: -(12-6y(y+7)), so:

12-6y(y+7)

determiningTheFunctionDomain
-6y(y+7)+12

We multiply parentheses

-6y^2-42y+12

Back to the equation:

-(-6y^2-42y+12)


We get rid of parentheses

6y^2+42y+2y-12+18=0

We add all the numbers together, and all the variables

6y^2+44y+6=0

a = 6; b = 44; c = +6;
Δ = b2-4ac
Δ = 442-4·6·6
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-16\sqrt{7}}{2*6}=\frac{-44-16\sqrt{7}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+16\sqrt{7}}{2*6}=\frac{-44+16\sqrt{7}}{12}
$