-4(-4y+6)-2y=2y(y-6)-9

Solution for -4(-4y+6)-2y=2y(y-6)-9 equation:

-4(-4y+6)-2y=2y(y-6)-9

We move all terms to the left:

-4(-4y+6)-2y-(2y(y-6)-9)=0

We add all the numbers together, and all the variables

-2y-4(-4y+6)-(2y(y-6)-9)=0

We multiply parentheses

-2y+16y-(2y(y-6)-9)-24=0


We calculate terms in parentheses: -(2y(y-6)-9), so:

2y(y-6)-9

We multiply parentheses

2y^2-12y-9

Back to the equation:

-(2y^2-12y-9)


We add all the numbers together, and all the variables

14y-(2y^2-12y-9)-24=0

We get rid of parentheses

-2y^2+14y+12y+9-24=0

We add all the numbers together, and all the variables

-2y^2+26y-15=0

a = -2; b = 26; c = -15;
Δ = b2-4ac
Δ = 262-4·(-2)·(-15)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{139}}{2*-2}=\frac{-26-2\sqrt{139}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{139}}{2*-2}=\frac{-26+2\sqrt{139}}{-4}
$