4(x-6)=-2(1/2x-4)

Solution for 4(x-6)=-2(1/2x-4) equation:

4(x-6)=-2(1/2x-4)

We move all terms to the left:

4(x-6)-(-2(1/2x-4))=0


Domain of the equation: 2x-4))!=0

x∈R


We multiply parentheses

4x-(-2(1/2x-4))-24=0

We multiply all the terms by the denominator


4x*2x-24*2x-4))-(-2(1-4))=0

We add all the numbers together, and all the variables

4x*2x-24*2x-4))-(-2(-3))=0

We add all the numbers together, and all the variables

4x*2x-24*2x=0

Wy multiply elements

8x^2-48x=0

a = 8; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·8·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*8}=\frac{96}{16}
=6
$