1/x-x=2

Solution for 1/x-x=2 equation:

1/x-x=2

We move all terms to the left:

1/x-x-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/x-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -1; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-1)·1
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{2}}{2*-1}=\frac{2-2\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{2}}{2*-1}=\frac{2+2\sqrt{2}}{-2}
$