7/3x-2/5x=1/15

Solution for 7/3x-2/5x=1/15 equation:

7/3x-2/5x=1/15

We move all terms to the left:

7/3x-2/5x-(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-2/5x-(+1/15)=0

We get rid of parentheses

7/3x-2/5x-1/15=0

We calculate fractions


(-75x^2)/225x^2+525x/225x^2+(-90x)/225x^2=0

We multiply all the terms by the denominator


(-75x^2)+525x+(-90x)=0

We get rid of parentheses

-75x^2+525x-90x=0

We add all the numbers together, and all the variables

-75x^2+435x=0

a = -75; b = 435; c = 0;
Δ = b2-4ac
Δ = 4352-4·(-75)·0
Δ = 189225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{189225}=435$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(435)-435}{2*-75}=\frac{-870}{-150}
=5+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(435)+435}{2*-75}=\frac{0}{-150}
=0
$