9/x+3=6/2x

Solution for 9/x+3=6/2x equation:

9/x+3=6/2x

We move all terms to the left:

9/x+3-(6/2x)=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

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

We get rid of parentheses

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

We calculate fractions


18x/2x^2+(-6x)/2x^2+3=0

We multiply all the terms by the denominator


18x+(-6x)+3*2x^2=0

Wy multiply elements

6x^2+18x+(-6x)=0

We get rid of parentheses

6x^2+18x-6x=0

We add all the numbers together, and all the variables

6x^2+12x=0

a = 6; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·6·0
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*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*6}=\frac{0}{12}
=0
$