20+y=20/y

Solution for 20+y=20/y equation:

20+y=20/y

We move all terms to the left:

20+y-(20/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+20/y)+20=0

We get rid of parentheses

y-20/y+20=0

We multiply all the terms by the denominator


y*y+20*y-20=0

We add all the numbers together, and all the variables

20y+y*y-20=0

Wy multiply elements

y^2+20y-20=0

a = 1; b = 20; c = -20;
Δ = b2-4ac
Δ = 202-4·1·(-20)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{30}}{2*1}=\frac{-20-4\sqrt{30}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{30}}{2*1}=\frac{-20+4\sqrt{30}}{2}
$