24(1/3x-4)=24(1/8X+1)

Solution for 24(1/3x-4)=24(1/8X+1) equation:

24(1/3x-4)=24(1/8x+1)

We move all terms to the left:

24(1/3x-4)-(24(1/8x+1))=0


Domain of the equation: 3x-4)!=0

x∈R



Domain of the equation: 8x+1))!=0

x∈R


We multiply parentheses

24x-(24(1/8x+1))-96=0

We multiply all the terms by the denominator


24x*8x-96*8x+1))-(24(1+1))=0

We add all the numbers together, and all the variables

24x*8x-96*8x+1))-(242)=0

We add all the numbers together, and all the variables

24x*8x-96*8x=0

Wy multiply elements

192x^2-768x=0

a = 192; b = -768; c = 0;
Δ = b2-4ac
Δ = -7682-4·192·0
Δ = 589824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{589824}=768$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-768)-768}{2*192}=\frac{0}{384}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-768)+768}{2*192}=\frac{1536}{384}
=4
$