(2x-1)(2x-1)=(x+1)

Solution for (2x-1)(2x-1)=(x+1) equation:

(2x-1)(2x-1)=(x+1)

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((x+1)), so:

(x+1)

We get rid of parentheses

x+1

Back to the equation:

-(x+1)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-5x=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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