3x/x+1+6/2x=7/x

Solution for 3x/x+1+6/2x=7/x equation:

3x/x+1+6/2x=7/x

We move all terms to the left:

3x/x+1+6/2x-(7/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x/x+6/2x-(+7/x)+1=0

We get rid of parentheses

3x/x+6/2x-7/x+1=0

We calculate fractions


(-11x)/2x^2+6x/2x^2+1=0

We multiply all the terms by the denominator


(-11x)+6x+1*2x^2=0

We add all the numbers together, and all the variables

6x+(-11x)+1*2x^2=0

Wy multiply elements

2x^2+6x+(-11x)=0

We get rid of parentheses

2x^2+6x-11x=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{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$