80/y+4y=60

Solution for 80/y+4y=60 equation:

80/y+4y=60

We move all terms to the left:

80/y+4y-(60)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

4y+80/y-60=0

We multiply all the terms by the denominator


4y*y-60*y+80=0

We add all the numbers together, and all the variables

-60y+4y*y+80=0

Wy multiply elements

4y^2-60y+80=0

a = 4; b = -60; c = +80;
Δ = b2-4ac
Δ = -602-4·4·80
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{145}}{2*4}=\frac{60-4\sqrt{145}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{145}}{2*4}=\frac{60+4\sqrt{145}}{8}
$