3/x+1=1/2X=

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

3/x+1=1/2x=

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


6x+(-1x)+1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

2x^2+6x-1x=0

We add all the numbers together, and all the variables

2x^2+5x=0

a = 2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*2}=\frac{0}{4}
=0
$