1/3x-1/4x=1/24

Solution for 1/3x-1/4x=1/24 equation:

1/3x-1/4x=1/24

We move all terms to the left:

1/3x-1/4x-(1/24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/4x-(+1/24)=0

We get rid of parentheses

1/3x-1/4x-1/24=0

We calculate fractions


(-48x^2)/576x^2+192x/576x^2+(-144x)/576x^2=0

We multiply all the terms by the denominator


(-48x^2)+192x+(-144x)=0

We get rid of parentheses

-48x^2+192x-144x=0

We add all the numbers together, and all the variables

-48x^2+48x=0

a = -48; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-48)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-48}=\frac{-96}{-96}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-48}=\frac{0}{-96}
=0
$