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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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