10^x+(200/10^x)=30

Solution for 10^x+(200/10^x)=30 equation:

10^x+(200/10^x)=30

We move all terms to the left:

10^x+(200/10^x)-(30)=0


Domain of the equation: 10^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

10^x+200/10^x-30=0

We multiply all the terms by the denominator


10^x*10^x-30*10^x+200=0

Wy multiply elements

100x^2-300x+200=0

a = 100; b = -300; c = +200;
Δ = b2-4ac
Δ = -3002-4·100·200
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-100}{2*100}=\frac{200}{200}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+100}{2*100}=\frac{400}{200}
=2
$