2x+(5/x)=100

Solution for 2x+(5/x)=100 equation:

2x+(5/x)=100

We move all terms to the left:

2x+(5/x)-(100)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+(+5/x)-100=0

We get rid of parentheses

2x+5/x-100=0

We multiply all the terms by the denominator


2x*x-100*x+5=0

We add all the numbers together, and all the variables

-100x+2x*x+5=0

Wy multiply elements

2x^2-100x+5=0

a = 2; b = -100; c = +5;
Δ = b2-4ac
Δ = -1002-4·2·5
Δ = 9960
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:

$\sqrt{\Delta}=\sqrt{9960}=\sqrt{4*2490}=\sqrt{4}*\sqrt{2490}=2\sqrt{2490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2490}}{2*2}=\frac{100-2\sqrt{2490}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2490}}{2*2}=\frac{100+2\sqrt{2490}}{4}
$