2x+(16/x)=40

Solution for 2x+(16/x)=40 equation:

2x+(16/x)=40

We move all terms to the left:

2x+(16/x)-(40)=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+(+16/x)-40=0

We get rid of parentheses

2x+16/x-40=0

We multiply all the terms by the denominator


2x*x-40*x+16=0

We add all the numbers together, and all the variables

-40x+2x*x+16=0

Wy multiply elements

2x^2-40x+16=0

a = 2; b = -40; c = +16;
Δ = b2-4ac
Δ = -402-4·2·16
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{23}}{2*2}=\frac{40-8\sqrt{23}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{23}}{2*2}=\frac{40+8\sqrt{23}}{4}
$