2(2^2y-1)-5(2y)+4=0

Solution for 2(2^2y-1)-5(2y)+4=0 equation:

2(2^2y-1)-5(2y)+4=0

We add all the numbers together, and all the variables

-52y+2(2^2y-1)+4=0

We multiply parentheses

4y^2-52y-2+4=0

We add all the numbers together, and all the variables

4y^2-52y+2=0

a = 4; b = -52; c = +2;
Δ = b2-4ac
Δ = -522-4·4·2
Δ = 2672
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:

$\sqrt{\Delta}=\sqrt{2672}=\sqrt{16*167}=\sqrt{16}*\sqrt{167}=4\sqrt{167}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{167}}{2*4}=\frac{52-4\sqrt{167}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{167}}{2*4}=\frac{52+4\sqrt{167}}{8}
$