3/x=x-2

Solution for 3/x=x-2 equation:

3/x=x-2

We move all terms to the left:

3/x-(x-2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3/x-x+2=0

We multiply all the terms by the denominator


-x*x+2*x+3=0

We add all the numbers together, and all the variables

2x-x*x+3=0

Wy multiply elements

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

a = -1; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-1)·3
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{-(2)-4}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*-1}=\frac{2}{-2}
=-1
$