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

Solution for (X-1)(x+1)+1+x=0 equation:

(X-1)(X+1)+1+X=0

We add all the numbers together, and all the variables

X+(X-1)(X+1)+1=0

We use the square of the difference formula

X^2+X-1+1=0

We add all the numbers together, and all the variables

X^2+X=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1}=\frac{0}{2}
=0
$