1/5x=1/13x+8

Solution for 1/5x=1/13x+8 equation:

1/5x=1/13x+8

We move all terms to the left:

1/5x-(1/13x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 13x+8)!=0

x∈R


We get rid of parentheses

1/5x-1/13x-8=0

We calculate fractions


13x/65x^2+(-5x)/65x^2-8=0

We multiply all the terms by the denominator


13x+(-5x)-8*65x^2=0

Wy multiply elements

-520x^2+13x+(-5x)=0

We get rid of parentheses

-520x^2+13x-5x=0

We add all the numbers together, and all the variables

-520x^2+8x=0

a = -520; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-520)·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*-520}=\frac{-16}{-1040}
=1/65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-520}=\frac{0}{-1040}
=0
$