4/3x-1=6/x-9

Solution for 4/3x-1=6/x-9 equation:

4/3x-1=6/x-9

We move all terms to the left:

4/3x-1-(6/x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/3x-6/x+9-1=0

We calculate fractions


4x/3x^2+(-18x)/3x^2+9-1=0

We add all the numbers together, and all the variables

4x/3x^2+(-18x)/3x^2+8=0

We multiply all the terms by the denominator


4x+(-18x)+8*3x^2=0

Wy multiply elements

24x^2+4x+(-18x)=0

We get rid of parentheses

24x^2+4x-18x=0

We add all the numbers together, and all the variables

24x^2-14x=0

a = 24; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·24·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*24}=\frac{28}{48}
=7/12
$