10^x=20/x

Solution for 10^x=20/x equation:

10^x=20/x

We move all terms to the left:

10^x-(20/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10^x-(+20/x)=0

We get rid of parentheses

10^x-20/x=0

We multiply all the terms by the denominator


10^x*x-20=0

Wy multiply elements

10x^2-20=0

a = 10; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·10·(-20)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*10}=\frac{0-20\sqrt{2}}{20}
=-\frac{20\sqrt{2}}{20}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*10}=\frac{0+20\sqrt{2}}{20}
=\frac{20\sqrt{2}}{20}
=\sqrt{2}
$