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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


x^2/2x^2+(-2x)/2x^2-3+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


x^2+(-2x)+3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-2x=0

a = 7; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·7·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*7}=\frac{0}{14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*7}=\frac{4}{14}
=2/7
$