6/x=9/8x+9

Solution for 6/x=9/8x+9 equation:

6/x=9/8x+9

We move all terms to the left:

6/x-(9/8x+9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x+9)!=0

x∈R


We get rid of parentheses

6/x-9/8x-9=0

We calculate fractions


48x/8x^2+(-9x)/8x^2-9=0

We multiply all the terms by the denominator


48x+(-9x)-9*8x^2=0

Wy multiply elements

-72x^2+48x+(-9x)=0

We get rid of parentheses

-72x^2+48x-9x=0

We add all the numbers together, and all the variables

-72x^2+39x=0

a = -72; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-72)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-72}=\frac{-78}{-144}
=13/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-72}=\frac{0}{-144}
=0
$