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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(2(x-1)(x-1)), so:

2(x-1)(x-1)

We multiply parentheses ..

2(+x^2-1x-1x+1)

We multiply parentheses

2x^2-2x-2x+2

We add all the numbers together, and all the variables

2x^2-4x+2

Back to the equation:

-(2x^2-4x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+6x-1=0

a = -1; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-1)·(-1)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{2}}{2*-1}=\frac{-6-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{2}}{2*-1}=\frac{-6+4\sqrt{2}}{-2}
$