-2y(3y-6)+9y=6+6(2y-1)

Solution for -2y(3y-6)+9y=6+6(2y-1) equation:

-2y(3y-6)+9y=6+6(2y-1)

We move all terms to the left:

-2y(3y-6)+9y-(6+6(2y-1))=0

We add all the numbers together, and all the variables

9y-2y(3y-6)-(6+6(2y-1))=0

We multiply parentheses

-6y^2+9y+12y-(6+6(2y-1))=0


We calculate terms in parentheses: -(6+6(2y-1)), so:

6+6(2y-1)

determiningTheFunctionDomain
6(2y-1)+6

We multiply parentheses

12y-6+6

We add all the numbers together, and all the variables

12y

Back to the equation:

-(12y)


We add all the numbers together, and all the variables

-6y^2+9y=0

a = -6; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-6)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-6}=\frac{0}{-12}
=0
$