1/3+1/4x=1/3x+4

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

1/3+1/4x=1/3x+4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


27x/108x^2+(-4x)/108x^2+4x/108x^2-4=0

We multiply all the terms by the denominator


27x+(-4x)+4x-4*108x^2=0

We add all the numbers together, and all the variables

31x+(-4x)-4*108x^2=0

Wy multiply elements

-432x^2+31x+(-4x)=0

We get rid of parentheses

-432x^2+31x-4x=0

We add all the numbers together, and all the variables

-432x^2+27x=0

a = -432; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-432)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-432}=\frac{-54}{-864}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-432}=\frac{0}{-864}
=0
$