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

Solution for 2(3x-4)=4(1/8x-8) equation:

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

We move all terms to the left:

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


Domain of the equation: 8x-8))!=0

x∈R


We multiply parentheses

6x-(4(1/8x-8))-8=0

We multiply all the terms by the denominator


6x*8x-8*8x-8))-(4(1-8))=0

We add all the numbers together, and all the variables

6x*8x-8*8x-8))-(4(-7))=0

We add all the numbers together, and all the variables

6x*8x-8*8x=0

Wy multiply elements

48x^2-64x=0

a = 48; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·48·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*48}=\frac{128}{96}
=1+1/3
$