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

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

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

x^2-2x=0

a = 1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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