(1/5x)-(7/3x)=1

Solution for (1/5x)-(7/3x)=1 equation:

(1/5x)-(7/3x)=1

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

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

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

We get rid of parentheses

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

We calculate fractions


3x/15x^2+(-35x)/15x^2-1=0

We multiply all the terms by the denominator


3x+(-35x)-1*15x^2=0

Wy multiply elements

-15x^2+3x+(-35x)=0

We get rid of parentheses

-15x^2+3x-35x=0

We add all the numbers together, and all the variables

-15x^2-32x=0

a = -15; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-15)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-15}=\frac{64}{-30}
=-2+2/15
$