x=3/x-2

Solution for x=3/x-2 equation:

x=3/x-2

We move all terms to the left:

x-(3/x-2)=0


Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x-3/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

x^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
$