-1/3x-1/2=-1/5x-1

Solution for -1/3x-1/2=-1/5x-1 equation:

-1/3x-1/2=-1/5x-1

We move all terms to the left:

-1/3x-1/2-(-1/5x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

-1/3x+1/5x+1-1/2=0

We calculate fractions


(-75x^2)/60x^2+(-20x)/60x^2+12x/60x^2+1=0

We multiply all the terms by the denominator


(-75x^2)+(-20x)+12x+1*60x^2=0

We add all the numbers together, and all the variables

(-75x^2)+12x+(-20x)+1*60x^2=0

Wy multiply elements

(-75x^2)+60x^2+12x+(-20x)=0

We get rid of parentheses

-75x^2+60x^2+12x-20x=0

We add all the numbers together, and all the variables

-15x^2-8x=0

a = -15; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-15)·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*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-15}=\frac{16}{-30}
=-8/15
$