240/y+y=120

Solution for 240/y+y=120 equation:

240/y+y=120

We move all terms to the left:

240/y+y-(120)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+240/y-120=0

We multiply all the terms by the denominator


y*y-120*y+240=0

We add all the numbers together, and all the variables

-120y+y*y+240=0

Wy multiply elements

y^2-120y+240=0

a = 1; b = -120; c = +240;
Δ = b2-4ac
Δ = -1202-4·1·240
Δ = 13440
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:

$\sqrt{\Delta}=\sqrt{13440}=\sqrt{64*210}=\sqrt{64}*\sqrt{210}=8\sqrt{210}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{210}}{2*1}=\frac{120-8\sqrt{210}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{210}}{2*1}=\frac{120+8\sqrt{210}}{2}
$