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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x-2x*x+4=0

Wy multiply elements

-2x^2-4x+4=0

a = -2; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-2)·4
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*-2}=\frac{4-4\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*-2}=\frac{4+4\sqrt{3}}{-4}
$