2(x+16)=72/x

Solution for 2(x+16)=72/x equation:

2(x+16)=72/x

We move all terms to the left:

2(x+16)-(72/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

2(x+16)-(+72/x)=0

We multiply parentheses

2x-(+72/x)+32=0

We get rid of parentheses

2x-72/x+32=0

We multiply all the terms by the denominator


2x*x+32*x-72=0

We add all the numbers together, and all the variables

32x+2x*x-72=0

Wy multiply elements

2x^2+32x-72=0

a = 2; b = 32; c = -72;
Δ = b2-4ac
Δ = 322-4·2·(-72)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-40}{2*2}=\frac{-72}{4}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+40}{2*2}=\frac{8}{4}
=2
$