-3(6y-8)-y=-3y(y-2)

Solution for -3(6y-8)-y=-3y(y-2) equation:

-3(6y-8)-y=-3y(y-2)

We move all terms to the left:

-3(6y-8)-y-(-3y(y-2))=0

We add all the numbers together, and all the variables

-1y-3(6y-8)-(-3y(y-2))=0

We multiply parentheses

-1y-18y-(-3y(y-2))+24=0


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

-3y(y-2)

We multiply parentheses

-3y^2+6y

Back to the equation:

-(-3y^2+6y)


We add all the numbers together, and all the variables

-(-3y^2+6y)-19y+24=0

We get rid of parentheses

3y^2-6y-19y+24=0

We add all the numbers together, and all the variables

3y^2-25y+24=0

a = 3; b = -25; c = +24;
Δ = b2-4ac
Δ = -252-4·3·24
Δ = 337
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{-(-25)-\sqrt{337}}{2*3}=\frac{25-\sqrt{337}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{337}}{2*3}=\frac{25+\sqrt{337}}{6}
$