2/3x+1/4=1/8x

Solution for 2/3x+1/4=1/8x equation:

2/3x+1/4=1/8x

We move all terms to the left:

2/3x+1/4-(1/8x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(+1/8x)+1/4=0

We get rid of parentheses

2/3x-1/8x+1/4=0

We calculate fractions


192x^2/384x^2+256x/384x^2+(-48x)/384x^2=0

We multiply all the terms by the denominator


192x^2+256x+(-48x)=0

We get rid of parentheses

192x^2+256x-48x=0

We add all the numbers together, and all the variables

192x^2+208x=0

a = 192; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·192·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*192}=\frac{-416}{384}
=-1+1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*192}=\frac{0}{384}
=0
$