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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))!=0We multiply parentheses

x∈R

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 = b^{2}-4ac

Δ = -64^{2}-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 $

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