6+1/x=14/2x

Solution for 6+1/x=14/2x equation:

6+1/x=14/2x

We move all terms to the left:

6+1/x-(14/2x)=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

1/x-(+14/2x)+6=0

We get rid of parentheses

1/x-14/2x+6=0

We calculate fractions


2x/2x^2+(-14x)/2x^2+6=0

We multiply all the terms by the denominator


2x+(-14x)+6*2x^2=0

Wy multiply elements

12x^2+2x+(-14x)=0

We get rid of parentheses

12x^2+2x-14x=0

We add all the numbers together, and all the variables

12x^2-12x=0

a = 12; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·12·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*12}=\frac{24}{24}
=1
$