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

Solution for 8(y-1)-3y=6y(2y-6) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

6y(2y-6)

We multiply parentheses

12y^2-36y

Back to the equation:

-(12y^2-36y)


We add all the numbers together, and all the variables

5y-(12y^2-36y)-8=0

We get rid of parentheses

-12y^2+5y+36y-8=0

We add all the numbers together, and all the variables

-12y^2+41y-8=0

a = -12; b = 41; c = -8;
Δ = b2-4ac
Δ = 412-4·(-12)·(-8)
Δ = 1297
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{-(41)-\sqrt{1297}}{2*-12}=\frac{-41-\sqrt{1297}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1297}}{2*-12}=\frac{-41+\sqrt{1297}}{-24}
$