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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3y^2+2y-6y+1=0

We add all the numbers together, and all the variables

3y^2-4y+1=0

a = 3; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·3·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*3}=\frac{2}{6}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*3}=\frac{6}{6}
=1
$