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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-135x^2+8x=0

a = -135; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-135)·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*-135}=\frac{-16}{-270}
=8/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-135}=\frac{0}{-270}
=0
$