x+6+x+6+1/2x+1/2x=24

Solution for x+6+x+6+1/2x+1/2x=24 equation:

x+6+x+6+1/2x+1/2x=24

We move all terms to the left:

x+6+x+6+1/2x+1/2x-(24)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-24x+2=0

a = 4; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·4·2
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{34}}{2*4}=\frac{24-4\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{34}}{2*4}=\frac{24+4\sqrt{34}}{8}
$