X=3x/X+2-2x+1

Solution for X=3x/X+2-2x+1 equation:

X=3X/X+2-2X+1

We move all terms to the left:

X-(3X/X+2-2X+1)=0


Domain of the equation: X+2-2X+1)!=0

We move all terms containing X to the left, all other terms to the right

X-2X+1)!=-2

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X+2X-3X/X-3=0

We multiply all the terms by the denominator


X*X+2X*X-3X-3*X=0

We add all the numbers together, and all the variables

-6X+X*X+2X*X=0

Wy multiply elements

X^2+2X^2-6X=0

We add all the numbers together, and all the variables

3X^2-6X=0

a = 3; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*3}=\frac{12}{6}
=2
$