5x=41/2x

Solution for 5x=41/2x equation:

5x=41/2x

We move all terms to the left:

5x-(41/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+41/2x)=0

We get rid of parentheses

5x-41/2x=0

We multiply all the terms by the denominator


5x*2x-41=0

Wy multiply elements

10x^2-41=0

a = 10; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·10·(-41)
Δ = 1640
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:

$\sqrt{\Delta}=\sqrt{1640}=\sqrt{4*410}=\sqrt{4}*\sqrt{410}=2\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{410}}{2*10}=\frac{0-2\sqrt{410}}{20}
=-\frac{2\sqrt{410}}{20}
=-\frac{\sqrt{410}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{410}}{2*10}=\frac{0+2\sqrt{410}}{20}
=\frac{2\sqrt{410}}{20}
=\frac{\sqrt{410}}{10}
$