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

Solution for (x+1/2x-1)-(x-1/x+2)=2 equation:

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

We move all terms to the left:

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


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

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

x/2x^2+2x/2x^2-5=0

We multiply all the terms by the denominator


x+2x-5*2x^2=0

We add all the numbers together, and all the variables

3x-5*2x^2=0

Wy multiply elements

-10x^2+3x=0

a = -10; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-10)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-10}=\frac{-6}{-20}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-10}=\frac{0}{-20}
=0
$