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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(3y+1)), so:

2(3y+1)

We multiply parentheses

6y+2

Back to the equation:

-(6y+2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

2y^2-3y-6y-2-3=0

We add all the numbers together, and all the variables

2y^2-9y-5=0

a = 2; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·2·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*2}=\frac{-2}{4}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*2}=\frac{20}{4}
=5
$