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)+32x+1*60x^2=0

Wy multiply elements

(-75x^2)+60x^2+32x=0

We get rid of parentheses

-75x^2+60x^2+32x=0

We add all the numbers together, and all the variables

-15x^2+32x=0

a = -15; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-15)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-15}=\frac{-64}{-30}
=2+2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-15}=\frac{0}{-30}
=0
$