36/y+y=20

Solution for 36/y+y=20 equation:

36/y+y=20

We move all terms to the left:

36/y+y-(20)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+36/y-20=0

We multiply all the terms by the denominator


y*y-20*y+36=0

We add all the numbers together, and all the variables

-20y+y*y+36=0

Wy multiply elements

y^2-20y+36=0

a = 1; b = -20; c = +36;
Δ = b2-4ac
Δ = -202-4·1·36
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*1}=\frac{4}{2}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*1}=\frac{36}{2}
=18
$