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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+x/2x+3=0

We calculate fractions


x^2/2x^2+4x/2x^2+3=0

We multiply all the terms by the denominator


x^2+4x+3*2x^2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

7x^2+4x=0

a = 7; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·7·0
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*7}=\frac{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*7}=\frac{0}{14}
=0
$