7/3x-1/3+3/5x=1/15

Solution for 7/3x-1/3+3/5x=1/15 equation:

7/3x-1/3+3/5x=1/15

We move all terms to the left:

7/3x-1/3+3/5x-(1/15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7/3x+3/5x-1/3-(+1/15)=0

We get rid of parentheses

7/3x+3/5x-1/3-1/15=0

We calculate fractions


(-225x^2)/2025x^2+525x/2025x^2+1215x/2025x^2+(-75x)/2025x^2=0

We multiply all the terms by the denominator


(-225x^2)+525x+1215x+(-75x)=0

We add all the numbers together, and all the variables

(-225x^2)+1740x+(-75x)=0

We get rid of parentheses

-225x^2+1740x-75x=0

We add all the numbers together, and all the variables

-225x^2+1665x=0

a = -225; b = 1665; c = 0;
Δ = b2-4ac
Δ = 16652-4·(-225)·0
Δ = 2772225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2772225}=1665$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1665)-1665}{2*-225}=\frac{-3330}{-450}
=7+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1665)+1665}{2*-225}=\frac{0}{-450}
=0
$