(2a-1)(2a-1)=a

Solution for (2a-1)(2a-1)=a equation:

(2a-1)(2a-1)=a

We move all terms to the left:

(2a-1)(2a-1)-(a)=0

We add all the numbers together, and all the variables

-1a+(2a-1)(2a-1)=0

We multiply parentheses ..

(+4a^2-2a-2a+1)-1a=0

We get rid of parentheses

4a^2-2a-2a-1a+1=0

We add all the numbers together, and all the variables

4a^2-5a+1=0

a = 4; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·4·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*4}=\frac{2}{8}
=1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*4}=\frac{8}{8}
=1
$