x=1/2(24x)

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

x=1/2(24x)

We move all terms to the left:

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


Domain of the equation: 224x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/224x)=0

We get rid of parentheses

x-1/224x=0

We multiply all the terms by the denominator


x*224x-1=0

Wy multiply elements

224x^2-1=0

a = 224; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·224·(-1)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*224}=\frac{0-8\sqrt{14}}{448}
=-\frac{8\sqrt{14}}{448}
=-\frac{\sqrt{14}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*224}=\frac{0+8\sqrt{14}}{448}
=\frac{8\sqrt{14}}{448}
=\frac{\sqrt{14}}{56}
$