x+8/12=1-3x/4x

Solution for x+8/12=1-3x/4x equation:

x+8/12=1-3x/4x

We move all terms to the left:

x+8/12-(1-3x/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-3x/4x+1)+8/12=0

We get rid of parentheses

x+3x/4x-1+8/12=0

We calculate fractions


x+36x/48x+32x/48x-1=0

We multiply all the terms by the denominator


x*48x+36x+32x-1*48x=0

We add all the numbers together, and all the variables

68x+x*48x-1*48x=0

Wy multiply elements

48x^2+68x-48x=0

We add all the numbers together, and all the variables

48x^2+20x=0

a = 48; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·48·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*48}=\frac{-40}{96}
=-5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*48}=\frac{0}{96}
=0
$