8+10/7x=6+5/1x

Solution for 8+10/7x=6+5/1x equation:

8+10/7x=6+5/1x

We move all terms to the left:

8+10/7x-(6+5/1x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 1x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10/7x-(5/1x+6)+8=0

We get rid of parentheses

10/7x-5/1x-6+8=0

We calculate fractions


10x/7x^2+(-35x)/7x^2-6+8=0

We add all the numbers together, and all the variables

10x/7x^2+(-35x)/7x^2+2=0

We multiply all the terms by the denominator


10x+(-35x)+2*7x^2=0

Wy multiply elements

14x^2+10x+(-35x)=0

We get rid of parentheses

14x^2+10x-35x=0

We add all the numbers together, and all the variables

14x^2-25x=0

a = 14; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·14·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*14}=\frac{50}{28}
=1+11/14
$