x+2x+1/2x=224

Solution for x+2x+1/2x=224 equation:

x+2x+1/2x=224

We move all terms to the left:

x+2x+1/2x-(224)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-224=0

We multiply all the terms by the denominator


3x*2x-224*2x+1=0

Wy multiply elements

6x^2-448x+1=0

a = 6; b = -448; c = +1;
Δ = b2-4ac
Δ = -4482-4·6·1
Δ = 200680
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:

$\sqrt{\Delta}=\sqrt{200680}=\sqrt{4*50170}=\sqrt{4}*\sqrt{50170}=2\sqrt{50170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-448)-2\sqrt{50170}}{2*6}=\frac{448-2\sqrt{50170}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-448)+2\sqrt{50170}}{2*6}=\frac{448+2\sqrt{50170}}{12}
$