y+(47/y)=97

Solution for y+(47/y)=97 equation:

y+(47/y)=97

We move all terms to the left:

y+(47/y)-(97)=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+(+47/y)-97=0

We get rid of parentheses

y+47/y-97=0

We multiply all the terms by the denominator


y*y-97*y+47=0

We add all the numbers together, and all the variables

-97y+y*y+47=0

Wy multiply elements

y^2-97y+47=0

a = 1; b = -97; c = +47;
Δ = b2-4ac
Δ = -972-4·1·47
Δ = 9221
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-\sqrt{9221}}{2*1}=\frac{97-\sqrt{9221}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+\sqrt{9221}}{2*1}=\frac{97+\sqrt{9221}}{2}
$