4/y+y=16

Solution for 4/y+y=16 equation:

4/y+y=16

We move all terms to the left:

4/y+y-(16)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+4/y-16=0

We multiply all the terms by the denominator


y*y-16*y+4=0

We add all the numbers together, and all the variables

-16y+y*y+4=0

Wy multiply elements

y^2-16y+4=0

a = 1; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·1·4
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{15}}{2*1}=\frac{16-4\sqrt{15}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{15}}{2*1}=\frac{16+4\sqrt{15}}{2}
$