3(2y-1)-2y(y-2)=-4(y+3)

Solution for 3(2y-1)-2y(y-2)=-4(y+3) equation:

3(2y-1)-2y(y-2)=-4(y+3)

We move all terms to the left:

3(2y-1)-2y(y-2)-(-4(y+3))=0

We multiply parentheses

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


We calculate terms in parentheses: -(-4(y+3)), so:

-4(y+3)

We multiply parentheses

-4y-12

Back to the equation:

-(-4y-12)


We add all the numbers together, and all the variables

-2y^2+10y-(-4y-12)-3=0

We get rid of parentheses

-2y^2+10y+4y+12-3=0

We add all the numbers together, and all the variables

-2y^2+14y+9=0

a = -2; b = 14; c = +9;
Δ = b2-4ac
Δ = 142-4·(-2)·9
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{67}}{2*-2}=\frac{-14-2\sqrt{67}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{67}}{2*-2}=\frac{-14+2\sqrt{67}}{-4}
$