100x=3.78/x

Solution for 100x=3.78/x equation:

100x=3.78/x

We move all terms to the left:

100x-(3.78/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

100x-(+3.78/x)=0

We get rid of parentheses

100x-3.78/x=0

We multiply all the terms by the denominator


100x*x-3.78=0

Wy multiply elements

100x^2-3.78=0

a = 100; b = 0; c = -3.78;
Δ = b2-4ac
Δ = 02-4·100·(-3.78)
Δ = 1512
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:

$\sqrt{\Delta}=\sqrt{1512}=\sqrt{36*42}=\sqrt{36}*\sqrt{42}=6\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{42}}{2*100}=\frac{0-6\sqrt{42}}{200}
=-\frac{6\sqrt{42}}{200}
=-\frac{3\sqrt{42}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{42}}{2*100}=\frac{0+6\sqrt{42}}{200}
=\frac{6\sqrt{42}}{200}
=\frac{3\sqrt{42}}{100}
$