2(6x-12)=24(1/2x+1)-2

Solution for 2(6x-12)=24(1/2x+1)-2 equation:

2(6x-12)=24(1/2x+1)-2

We move all terms to the left:

2(6x-12)-(24(1/2x+1)-2)=0


Domain of the equation: 2x+1)-2)!=0

x∈R


We multiply parentheses

12x-(24(1/2x+1)-2)-24=0

We multiply all the terms by the denominator


12x*2x-24*2x+1)-2)-(24(1+1)-2)=0

We add all the numbers together, and all the variables

12x*2x-24*2x+1)-2)-(242-2)=0

We add all the numbers together, and all the variables

12x*2x-24*2x=0

Wy multiply elements

24x^2-48x=0

a = 24; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·24·0
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*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*24}=\frac{96}{48}
=2
$