15x+200=300/x

Solution for 15x+200=300/x equation:

15x+200=300/x

We move all terms to the left:

15x+200-(300/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

15x-(+300/x)+200=0

We get rid of parentheses

15x-300/x+200=0

We multiply all the terms by the denominator


15x*x+200*x-300=0

We add all the numbers together, and all the variables

200x+15x*x-300=0

Wy multiply elements

15x^2+200x-300=0

a = 15; b = 200; c = -300;
Δ = b2-4ac
Δ = 2002-4·15·(-300)
Δ = 58000
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:

$\sqrt{\Delta}=\sqrt{58000}=\sqrt{400*145}=\sqrt{400}*\sqrt{145}=20\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-20\sqrt{145}}{2*15}=\frac{-200-20\sqrt{145}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+20\sqrt{145}}{2*15}=\frac{-200+20\sqrt{145}}{30}
$