5/x=8/7x+1

Solution for 5/x=8/7x+1 equation:

5/x=8/7x+1

We move all terms to the left:

5/x-(8/7x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x+1)!=0

x∈R


We get rid of parentheses

5/x-8/7x-1=0

We calculate fractions


35x/7x^2+(-8x)/7x^2-1=0

We multiply all the terms by the denominator


35x+(-8x)-1*7x^2=0

Wy multiply elements

-7x^2+35x+(-8x)=0

We get rid of parentheses

-7x^2+35x-8x=0

We add all the numbers together, and all the variables

-7x^2+27x=0

a = -7; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-7)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-7}=\frac{-54}{-14}
=3+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-7}=\frac{0}{-14}
=0
$