100x=3400/20x

Solution for 100x=3400/20x equation:

100x=3400/20x

We move all terms to the left:

100x-(3400/20x)=0


Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

100x-(+3400/20x)=0

We get rid of parentheses

100x-3400/20x=0

We multiply all the terms by the denominator


100x*20x-3400=0

Wy multiply elements

2000x^2-3400=0

a = 2000; b = 0; c = -3400;
Δ = b2-4ac
Δ = 02-4·2000·(-3400)
Δ = 27200000
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:

$\sqrt{\Delta}=\sqrt{27200000}=\sqrt{160000*170}=\sqrt{160000}*\sqrt{170}=400\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{170}}{2*2000}=\frac{0-400\sqrt{170}}{4000}
=-\frac{400\sqrt{170}}{4000}
=-\frac{\sqrt{170}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{170}}{2*2000}=\frac{0+400\sqrt{170}}{4000}
=\frac{400\sqrt{170}}{4000}
=\frac{\sqrt{170}}{10}
$