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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-8))!=0

x∈R


We multiply parentheses

6x-((1/2x-8))-8=0

We multiply all the terms by the denominator


6x*2x-8*2x-8))-((1-8))=0

We add all the numbers together, and all the variables

6x*2x-8*2x-8))-((-7))=0

We add all the numbers together, and all the variables

6x*2x-8*2x=0

Wy multiply elements

12x^2-16x=0

a = 12; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·12·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*12}=\frac{32}{24}
=1+1/3
$