2x+-3(x+4)=1/2x+6

Solution for 2x+-3(x+4)=1/2x+6 equation:

2x+-3(x+4)=1/2x+6

We move all terms to the left:

2x+-3(x+4)-(1/2x+6)=0


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

x∈R


We add all the numbers together, and all the variables

2x-3(x+4)-(1/2x+6)=0

We multiply parentheses

2x-3x-(1/2x+6)-12=0

We get rid of parentheses

2x-3x-1/2x-6-12=0

We multiply all the terms by the denominator


2x*2x-3x*2x-6*2x-12*2x-1=0

Wy multiply elements

4x^2-6x^2-12x-24x-1=0

We add all the numbers together, and all the variables

-2x^2-36x-1=0

a = -2; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·(-2)·(-1)
Δ = 1288
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:

$\sqrt{\Delta}=\sqrt{1288}=\sqrt{4*322}=\sqrt{4}*\sqrt{322}=2\sqrt{322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{322}}{2*-2}=\frac{36-2\sqrt{322}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{322}}{2*-2}=\frac{36+2\sqrt{322}}{-4}
$