9/x=5/3x-4

Solution for 9/x=5/3x-4 equation:

9/x=5/3x-4

We move all terms to the left:

9/x-(5/3x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

9/x-5/3x+4=0

We calculate fractions


27x/3x^2+(-5x)/3x^2+4=0

We multiply all the terms by the denominator


27x+(-5x)+4*3x^2=0

Wy multiply elements

12x^2+27x+(-5x)=0

We get rid of parentheses

12x^2+27x-5x=0

We add all the numbers together, and all the variables

12x^2+22x=0

a = 12; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·12·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*12}=\frac{-44}{24}
=-1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*12}=\frac{0}{24}
=0
$