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

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

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

We move all terms to the left:

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


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

x∈R


We multiply parentheses

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

We get rid of parentheses

2x+4x-1/2x+2-4=0

We multiply all the terms by the denominator


2x*2x+4x*2x+2*2x-4*2x-1=0

Wy multiply elements

4x^2+8x^2+4x-8x-1=0

We add all the numbers together, and all the variables

12x^2-4x-1=0

a = 12; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·12·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*12}=\frac{-4}{24}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*12}=\frac{12}{24}
=1/2
$