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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3y^2-2y-3y+1=0

We add all the numbers together, and all the variables

3y^2-5y+1=0

a = 3; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·3·1
Δ = 13
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{-(-5)-\sqrt{13}}{2*3}=\frac{5-\sqrt{13}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*3}=\frac{5+\sqrt{13}}{6}
$