1/x+1/3x=4

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

1/x+1/3x=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4x-4*3x^2=0

Wy multiply elements

-12x^2+4x=0

a = -12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-12}=\frac{-8}{-24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-12}=\frac{0}{-24}
=0
$