4y^2-5y+1=1

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

4y^2-5y+1=1

We move all terms to the left:

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

We add all the numbers together, and all the variables

4y^2-5y=0

a = 4; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·4·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*4}=\frac{0}{8}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*4}=\frac{10}{8}
=1+1/4
$