1/3x-5/12=1/4x-1

Solution for 1/3x-5/12=1/4x-1 equation:

1/3x-5/12=1/4x-1

We move all terms to the left:

1/3x-5/12-(1/4x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

1/3x-1/4x+1-5/12=0

We calculate fractions


(-240x^2)/144x^2+48x/144x^2+(-36x)/144x^2+1=0

We multiply all the terms by the denominator


(-240x^2)+48x+(-36x)+1*144x^2=0

Wy multiply elements

(-240x^2)+144x^2+48x+(-36x)=0

We get rid of parentheses

-240x^2+144x^2+48x-36x=0

We add all the numbers together, and all the variables

-96x^2+12x=0

a = -96; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-96)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-96}=\frac{-24}{-192}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-96}=\frac{0}{-192}
=0
$