12-2(y+3)=4(y-6)(y-1)

Solution for 12-2(y+3)=4(y-6)(y-1) equation:

12-2(y+3)=4(y-6)(y-1)

We move all terms to the left:

12-2(y+3)-(4(y-6)(y-1))=0

We multiply parentheses

-2y-(4(y-6)(y-1))-6+12=0

We multiply parentheses ..

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


We calculate terms in parentheses: -(4(+y^2-1y-6y+6)), so:

4(+y^2-1y-6y+6)

We multiply parentheses

4y^2-4y-24y+24

We add all the numbers together, and all the variables

4y^2-28y+24

Back to the equation:

-(4y^2-28y+24)


We add all the numbers together, and all the variables

-2y-(4y^2-28y+24)+6=0

We get rid of parentheses

-4y^2-2y+28y-24+6=0

We add all the numbers together, and all the variables

-4y^2+26y-18=0

a = -4; b = 26; c = -18;
Δ = b2-4ac
Δ = 262-4·(-4)·(-18)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{97}}{2*-4}=\frac{-26-2\sqrt{97}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{97}}{2*-4}=\frac{-26+2\sqrt{97}}{-8}
$