2/x+4=6/2x-1

Solution for 2/x+4=6/2x-1 equation:

2/x+4=6/2x-1

We move all terms to the left:

2/x+4-(6/2x-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-6/2x+1+4=0

We calculate fractions


4x/2x^2+(-6x)/2x^2+1+4=0

We add all the numbers together, and all the variables

4x/2x^2+(-6x)/2x^2+5=0

We multiply all the terms by the denominator


4x+(-6x)+5*2x^2=0

Wy multiply elements

10x^2+4x+(-6x)=0

We get rid of parentheses

10x^2+4x-6x=0

We add all the numbers together, and all the variables

10x^2-2x=0

a = 10; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*10}=\frac{4}{20}
=1/5
$