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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(-1x-1)

We get rid of parentheses

-1x-1

Back to the equation:

-(-1x-1)


We get rid of parentheses

x^2+1x+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
$