3y(2y-1)=4y-2

Solution for 3y(2y-1)=4y-2 equation:

3y(2y-1)=4y-2

We move all terms to the left:

3y(2y-1)-(4y-2)=0

We multiply parentheses

6y^2-3y-(4y-2)=0

We get rid of parentheses

6y^2-3y-4y+2=0

We add all the numbers together, and all the variables

6y^2-7y+2=0

a = 6; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*6}=\frac{6}{12}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*6}=\frac{8}{12}
=2/3
$