(2y-3)(2y-1)=5y

Solution for (2y-3)(2y-1)=5y equation:

(2y-3)(2y-1)=5y

We move all terms to the left:

(2y-3)(2y-1)-(5y)=0

We add all the numbers together, and all the variables

-5y+(2y-3)(2y-1)=0

We multiply parentheses ..

(+4y^2-2y-6y+3)-5y=0

We get rid of parentheses

4y^2-2y-6y-5y+3=0

We add all the numbers together, and all the variables

4y^2-13y+3=0

a = 4; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·4·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*4}=\frac{2}{8}
=1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*4}=\frac{24}{8}
=3
$