5/7x-1/3x=8

Solution for 5/7x-1/3x=8 equation:

5/7x-1/3x=8

We move all terms to the left:

5/7x-1/3x-(8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x/21x^2+(-7x)/21x^2-8=0

We multiply all the terms by the denominator


15x+(-7x)-8*21x^2=0

Wy multiply elements

-168x^2+15x+(-7x)=0

We get rid of parentheses

-168x^2+15x-7x=0

We add all the numbers together, and all the variables

-168x^2+8x=0

a = -168; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-168)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-168}=\frac{-16}{-336}
=1/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-168}=\frac{0}{-336}
=0
$