9/x=11/3x-8

Solution for 9/x=11/3x-8 equation:

9/x=11/3x-8

We move all terms to the left:

9/x-(11/3x-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

9/x-11/3x+8=0

We calculate fractions


27x/3x^2+(-11x)/3x^2+8=0

We multiply all the terms by the denominator


27x+(-11x)+8*3x^2=0

Wy multiply elements

24x^2+27x+(-11x)=0

We get rid of parentheses

24x^2+27x-11x=0

We add all the numbers together, and all the variables

24x^2+16x=0

a = 24; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·24·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*24}=\frac{-32}{48}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*24}=\frac{0}{48}
=0
$