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

Solution for 3(x+2)=1/2x-6 equation:

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

We move all terms to the left:

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


Domain of the equation: 2x-6)!=0

x∈R


We multiply parentheses

3x-(1/2x-6)+6=0

We get rid of parentheses

3x-1/2x+6+6=0

We multiply all the terms by the denominator


3x*2x+6*2x+6*2x-1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2+24x-1=0

a = 6; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·6·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*6}=\frac{-24-10\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*6}=\frac{-24+10\sqrt{6}}{12}
$