2/x-3=x-2

Solution for 2/x-3=x-2 equation:

2/x-3=x-2

We move all terms to the left:

2/x-3-(x-2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-x+2-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1x-x*x+2=0

Wy multiply elements

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

a = -1; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-1}=\frac{4}{-2}
=-2
$