2(x+3)=1/2x+12

Solution for 2(x+3)=1/2x+12 equation:

2(x+3)=1/2x+12

We move all terms to the left:

2(x+3)-(1/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

2x-1/2x-12+6=0

We multiply all the terms by the denominator


2x*2x-12*2x+6*2x-1=0

Wy multiply elements

4x^2-24x+12x-1=0

We add all the numbers together, and all the variables

4x^2-12x-1=0

a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8}
$