15/2x=6/x+9

Solution for 15/2x=6/x+9 equation:

15/2x=6/x+9

We move all terms to the left:

15/2x-(6/x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+9)!=0

x∈R


We get rid of parentheses

15/2x-6/x-9=0

We calculate fractions


15x/2x^2+(-12x)/2x^2-9=0

We multiply all the terms by the denominator


15x+(-12x)-9*2x^2=0

Wy multiply elements

-18x^2+15x+(-12x)=0

We get rid of parentheses

-18x^2+15x-12x=0

We add all the numbers together, and all the variables

-18x^2+3x=0

a = -18; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-18)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-18}=\frac{-6}{-36}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-18}=\frac{0}{-36}
=0
$