X-2/x=-x

Solution for X-2/x=-x equation:

X-2/X=-X

We move all terms to the left:

X-2/X-(-X)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-2/X-(-1X)=0

We get rid of parentheses

X-2/X+1X=0

We multiply all the terms by the denominator


X*X+1X*X-2=0

Wy multiply elements

X^2+X^2-2=0

We add all the numbers together, and all the variables

2X^2-2=0

a = 2; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·2·(-2)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*2}=\frac{-4}{4}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*2}=\frac{4}{4}
=1
$