3/7x-1/5x=8

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

3/7x-1/5x=8

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


15x/35x^2+(-7x)/35x^2-8=0

We multiply all the terms by the denominator


15x+(-7x)-8*35x^2=0

Wy multiply elements

-280x^2+15x+(-7x)=0

We get rid of parentheses

-280x^2+15x-7x=0

We add all the numbers together, and all the variables

-280x^2+8x=0

a = -280; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-280)·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*-280}=\frac{-16}{-560}
=1/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-280}=\frac{0}{-560}
=0
$