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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

6y^2-12y-(-2y+8)=0

We get rid of parentheses

6y^2-12y+2y-8=0

We add all the numbers together, and all the variables

6y^2-10y-8=0

a = 6; b = -10; c = -8;
Δ = b2-4ac
Δ = -102-4·6·(-8)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{73}}{2*6}=\frac{10-2\sqrt{73}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{73}}{2*6}=\frac{10+2\sqrt{73}}{12}
$