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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1y-3(6y-3)-(-3y(y-4))=0

We multiply parentheses

-1y-18y-(-3y(y-4))+9=0


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

-3y(y-4)

We multiply parentheses

-3y^2+12y

Back to the equation:

-(-3y^2+12y)


We add all the numbers together, and all the variables

-(-3y^2+12y)-19y+9=0

We get rid of parentheses

3y^2-12y-19y+9=0

We add all the numbers together, and all the variables

3y^2-31y+9=0

a = 3; b = -31; c = +9;
Δ = b2-4ac
Δ = -312-4·3·9
Δ = 853
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{853}}{2*3}=\frac{31-\sqrt{853}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{853}}{2*3}=\frac{31+\sqrt{853}}{6}
$