10y-17=23/y

Solution for 10y-17=23/y equation:

10y-17=23/y

We move all terms to the left:

10y-17-(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

10y-(+23/y)-17=0

We get rid of parentheses

10y-23/y-17=0

We multiply all the terms by the denominator


10y*y-17*y-23=0

We add all the numbers together, and all the variables

-17y+10y*y-23=0

Wy multiply elements

10y^2-17y-23=0

a = 10; b = -17; c = -23;
Δ = b2-4ac
Δ = -172-4·10·(-23)
Δ = 1209
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{-(-17)-\sqrt{1209}}{2*10}=\frac{17-\sqrt{1209}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1209}}{2*10}=\frac{17+\sqrt{1209}}{20}
$