x+x+1/2x=24

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

x+x+1/2x=24

We move all terms to the left:

x+x+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-24=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-48x+1=0

a = 4; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·4·1
Δ = 2288
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:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{143}}{2*4}=\frac{48-4\sqrt{143}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{143}}{2*4}=\frac{48+4\sqrt{143}}{8}
$