5/3x-3/2x=1/9

Solution for 5/3x-3/2x=1/9 equation:

5/3x-3/2x=1/9

We move all terms to the left:

5/3x-3/2x-(1/9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-3/2x-(+1/9)=0

We get rid of parentheses

5/3x-3/2x-1/9=0

We calculate fractions


(-12x^2)/486x^2+810x/486x^2+(-729x)/486x^2=0

We multiply all the terms by the denominator


(-12x^2)+810x+(-729x)=0

We get rid of parentheses

-12x^2+810x-729x=0

We add all the numbers together, and all the variables

-12x^2+81x=0

a = -12; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-12)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-12}=\frac{-162}{-24}
=6+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-12}=\frac{0}{-24}
=0
$