50x=300/2x

Solution for 50x=300/2x equation:

50x=300/2x

We move all terms to the left:

50x-(300/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

50x-(+300/2x)=0

We get rid of parentheses

50x-300/2x=0

We multiply all the terms by the denominator


50x*2x-300=0

Wy multiply elements

100x^2-300=0

a = 100; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·100·(-300)
Δ = 120000
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:

$\sqrt{\Delta}=\sqrt{120000}=\sqrt{40000*3}=\sqrt{40000}*\sqrt{3}=200\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{3}}{2*100}=\frac{0-200\sqrt{3}}{200}
=-\frac{200\sqrt{3}}{200}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{3}}{2*100}=\frac{0+200\sqrt{3}}{200}
=\frac{200\sqrt{3}}{200}
=\sqrt{3}
$