3/5x-4/3x=22/15

Solution for 3/5x-4/3x=22/15 equation:

3/5x-4/3x=22/15

We move all terms to the left:

3/5x-4/3x-(22/15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-4/3x-(+22/15)=0

We get rid of parentheses

3/5x-4/3x-22/15=0

We calculate fractions


(-990x^2)/225x^2+135x/225x^2+(-300x)/225x^2=0

We multiply all the terms by the denominator


(-990x^2)+135x+(-300x)=0

We get rid of parentheses

-990x^2+135x-300x=0

We add all the numbers together, and all the variables

-990x^2-165x=0

a = -990; b = -165; c = 0;
Δ = b2-4ac
Δ = -1652-4·(-990)·0
Δ = 27225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27225}=165$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-165}{2*-990}=\frac{0}{-1980}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+165}{2*-990}=\frac{330}{-1980}
=-1/6
$