-2/x+4=2/2x-1

Solution for -2/x+4=2/2x-1 equation:

-2/x+4=2/2x-1

We move all terms to the left:

-2/x+4-(2/2x-1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

-2/x-2/2x+1+4=0

We calculate fractions


(-4x)/2x^2+(-2x)/2x^2+1+4=0

We add all the numbers together, and all the variables

(-4x)/2x^2+(-2x)/2x^2+5=0

We multiply all the terms by the denominator


(-4x)+(-2x)+5*2x^2=0

Wy multiply elements

10x^2+(-4x)+(-2x)=0

We get rid of parentheses

10x^2-4x-2x=0

We add all the numbers together, and all the variables

10x^2-6x=0

a = 10; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·10·0
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*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*10}=\frac{12}{20}
=3/5
$