1/3x-1/x=4

Solution for 1/3x-1/x=4 equation:

1/3x-1/x=4

We move all terms to the left:

1/3x-1/x-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


x/3x^2+(-3x)/3x^2-4=0

We multiply all the terms by the denominator


x+(-3x)-4*3x^2=0

Wy multiply elements

-12x^2+x+(-3x)=0

We get rid of parentheses

-12x^2+x-3x=0

We add all the numbers together, and all the variables

-12x^2-2x=0

a = -12; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-12)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-12}=\frac{4}{-24}
=-1/6
$