10x=1/2x

Solution for 10x=1/2x equation:

10x=1/2x

We move all terms to the left:

10x-(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

10x-(+1/2x)=0

We get rid of parentheses

10x-1/2x=0

We multiply all the terms by the denominator


10x*2x-1=0

Wy multiply elements

20x^2-1=0

a = 20; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·20·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*20}=\frac{0-4\sqrt{5}}{40}
=-\frac{4\sqrt{5}}{40}
=-\frac{\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*20}=\frac{0+4\sqrt{5}}{40}
=\frac{4\sqrt{5}}{40}
=\frac{\sqrt{5}}{10}
$