2y(y+4)=3-(6-3y)

Solution for 2y(y+4)=3-(6-3y) equation:

2y(y+4)=3-(6-3y)

We move all terms to the left:

2y(y+4)-(3-(6-3y))=0

We add all the numbers together, and all the variables

2y(y+4)-(3-(-3y+6))=0

We multiply parentheses

2y^2+8y-(3-(-3y+6))=0


We calculate terms in parentheses: -(3-(-3y+6)), so:

3-(-3y+6)

determiningTheFunctionDomain
-(-3y+6)+3

We get rid of parentheses

3y-6+3

We add all the numbers together, and all the variables

3y-3

Back to the equation:

-(3y-3)


We get rid of parentheses

2y^2+8y-3y+3=0

We add all the numbers together, and all the variables

2y^2+5y+3=0

a = 2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·2·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*2}=\frac{-6}{4}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*2}=\frac{-4}{4}
=-1
$