8-1/7x=6-1/5x

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

8-1/7x=6-1/5x

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-5x)/35x^2+7x/35x^2-6+8=0

We add all the numbers together, and all the variables

(-5x)/35x^2+7x/35x^2+2=0

We multiply all the terms by the denominator


(-5x)+7x+2*35x^2=0

We add all the numbers together, and all the variables

7x+(-5x)+2*35x^2=0

Wy multiply elements

70x^2+7x+(-5x)=0

We get rid of parentheses

70x^2+7x-5x=0

We add all the numbers together, and all the variables

70x^2+2x=0

a = 70; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·70·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*70}=\frac{-4}{140}
=-1/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*70}=\frac{0}{140}
=0
$