5/x+6=9/2x

Solution for 5/x+6=9/2x equation:

5/x+6=9/2x

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


10x/2x^2+(-9x)/2x^2+6=0

We multiply all the terms by the denominator


10x+(-9x)+6*2x^2=0

Wy multiply elements

12x^2+10x+(-9x)=0

We get rid of parentheses

12x^2+10x-9x=0

We add all the numbers together, and all the variables

12x^2+x=0

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

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