2/x=x/2x+1

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

2/x=x/2x+1

We move all terms to the left:

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+4x=0

a = -3; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-3)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-3}=\frac{0}{-6}
=0
$