6/5+5/(4x)=2/(3x)

Solution for 6/5+5/(4x)=2/(3x) equation:

6/5+5/(4x)=2/(3x)

We move all terms to the left:

6/5+5/(4x)-(2/(3x))=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(+2/3x)+6/5=0

We get rid of parentheses

5/4x-2/3x+6/5=0

We calculate fractions


216x^2/300x^2+375x/300x^2+(-200x)/300x^2=0

We multiply all the terms by the denominator


216x^2+375x+(-200x)=0

We get rid of parentheses

216x^2+375x-200x=0

We add all the numbers together, and all the variables

216x^2+175x=0

a = 216; b = 175; c = 0;
Δ = b2-4ac
Δ = 1752-4·216·0
Δ = 30625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30625}=175$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(175)-175}{2*216}=\frac{-350}{432}
=-175/216
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(175)+175}{2*216}=\frac{0}{432}
=0
$