(x+6)+2*1/2x=24

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

(x+6)+2*1/2x=24

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x+2*1/2x+6-24=0

We multiply all the terms by the denominator


x*2x+6*2x-24*2x+2*1=0

We add all the numbers together, and all the variables

x*2x+6*2x-24*2x+2=0

Wy multiply elements

2x^2+12x-48x+2=0

We add all the numbers together, and all the variables

2x^2-36x+2=0

a = 2; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·2·2
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{5}}{2*2}=\frac{36-16\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{5}}{2*2}=\frac{36+16\sqrt{5}}{4}
$