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

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

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

We move all terms to the left:

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


Domain of the equation: (x+2)!=0

We move all terms containing x to the left, all other terms to the right

x!=-2

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-3x+1=0

a = -1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-1)·1
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{13}}{2*-1}=\frac{3-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{13}}{2*-1}=\frac{3+\sqrt{13}}{-2}
$