6/x=8/7x+1

Solution for 6/x=8/7x+1 equation:

6/x=8/7x+1

We move all terms to the left:

6/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

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

We calculate fractions


42x/7x^2+(-8x)/7x^2-1=0

We multiply all the terms by the denominator


42x+(-8x)-1*7x^2=0

Wy multiply elements

-7x^2+42x+(-8x)=0

We get rid of parentheses

-7x^2+42x-8x=0

We add all the numbers together, and all the variables

-7x^2+34x=0

a = -7; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-7)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-7}=\frac{-68}{-14}
=4+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-7}=\frac{0}{-14}
=0
$