3x+2=2/x+1

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

3x+2=2/x+1

We move all terms to the left:

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


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+3x*x-2=0

Wy multiply elements

3x^2+x-2=0

a = 3; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·3·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*3}=\frac{4}{6}
=2/3
$