2x+24=1/2x

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

2x+24=1/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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 = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{145}}{2*4}=\frac{-48-4\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{145}}{2*4}=\frac{-48+4\sqrt{145}}{8}
$