-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

-384x^2-84x=0

a = -384; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·(-384)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*-384}=\frac{0}{-768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*-384}=\frac{168}{-768}
=-7/32
$