(2y+1)4y=2

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

(2y+1)4y=2

We move all terms to the left:

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

We multiply parentheses

8y^2+4y-2=0

a = 8; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·8·(-2)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{5}}{2*8}=\frac{-4-4\sqrt{5}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{5}}{2*8}=\frac{-4+4\sqrt{5}}{16}
$