0.66(9+6y)-2y=2y(y+3)

Solution for 0.66(9+6y)-2y=2y(y+3) equation:

0.66(9+6y)-2y=2y(y+3)

We move all terms to the left:

0.66(9+6y)-2y-(2y(y+3))=0

We add all the numbers together, and all the variables

0.66(6y+9)-2y-(2y(y+3))=0

We add all the numbers together, and all the variables

-2y+0.66(6y+9)-(2y(y+3))=0

We multiply parentheses

-2y+3.96y-(2y(y+3))+5.94=0


We calculate terms in parentheses: -(2y(y+3)), so:

2y(y+3)

We multiply parentheses

2y^2+6y

Back to the equation:

-(2y^2+6y)


We add all the numbers together, and all the variables

1.96y-(2y^2+6y)+5.94=0

We get rid of parentheses

-2y^2+1.96y-6y+5.94=0

We add all the numbers together, and all the variables

-2y^2-4.04y+5.94=0

a = -2; b = -4.04; c = +5.94;
Δ = b2-4ac
Δ = -4.042-4·(-2)·5.94
Δ = 63.8416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4.04)-\sqrt{63.8416}}{2*-2}=\frac{4.04-\sqrt{63.8416}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.04)+\sqrt{63.8416}}{2*-2}=\frac{4.04+\sqrt{63.8416}}{-4}
$