2y(4y+1)=3y

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

2y(4y+1)=3y

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8y^2-3y+2y=0

We add all the numbers together, and all the variables

8y^2-1y=0

a = 8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·8·0
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{-(-1)-1}{2*8}=\frac{0}{16}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*8}=\frac{2}{16}
=1/8
$