0=x+2/x-3

Solution for 0=x+2/x-3 equation:

0=x+2/x-3

We move all terms to the left:

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


Domain of the equation: x-3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-2/x+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x-x*x-2=0

Wy multiply elements

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

a = -1; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·(-1)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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