5-1/5x=1/15x

Solution for 5-1/5x=1/15x equation:

5-1/5x=1/15x

We move all terms to the left:

5-1/5x-(1/15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/5x-(+1/15x)+5=0

We get rid of parentheses

-1/5x-1/15x+5=0

We calculate fractions


(-15x)/75x^2+(-5x)/75x^2+5=0

We multiply all the terms by the denominator


(-15x)+(-5x)+5*75x^2=0

Wy multiply elements

375x^2+(-15x)+(-5x)=0

We get rid of parentheses

375x^2-15x-5x=0

We add all the numbers together, and all the variables

375x^2-20x=0

a = 375; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·375·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*375}=\frac{0}{750}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*375}=\frac{40}{750}
=4/75
$