37-y=23/y

Solution for 37-y=23/y equation:

37-y=23/y

We move all terms to the left:

37-y-(23/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-(+23/y)+37=0

We add all the numbers together, and all the variables

-1y-(+23/y)+37=0

We get rid of parentheses

-1y-23/y+37=0

We multiply all the terms by the denominator


-1y*y+37*y-23=0

We add all the numbers together, and all the variables

37y-1y*y-23=0

Wy multiply elements

-1y^2+37y-23=0

a = -1; b = 37; c = -23;
Δ = b2-4ac
Δ = 372-4·(-1)·(-23)
Δ = 1277
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{-(37)-\sqrt{1277}}{2*-1}=\frac{-37-\sqrt{1277}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{1277}}{2*-1}=\frac{-37+\sqrt{1277}}{-2}
$