16/r+16r=40

Solution for 16/r+16r=40 equation:

16/r+16r=40

We move all terms to the left:

16/r+16r-(40)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

16r+16/r-40=0

We multiply all the terms by the denominator


16r*r-40*r+16=0

We add all the numbers together, and all the variables

-40r+16r*r+16=0

Wy multiply elements

16r^2-40r+16=0

a = 16; b = -40; c = +16;
Δ = b2-4ac
Δ = -402-4·16·16
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-24}{2*16}=\frac{16}{32}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+24}{2*16}=\frac{64}{32}
=2
$