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

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

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

We move all terms to the left:

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


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

x∈R


We multiply all the terms by the denominator


2x*2x-6*2x+2))-(4(1+2))=0

We add all the numbers together, and all the variables

2x*2x-6*2x+2))-(43)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-12x=0

a = 4; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·4·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*4}=\frac{24}{8}
=3
$