12y-7=113/y

Solution for 12y-7=113/y equation:

12y-7=113/y

We move all terms to the left:

12y-7-(113/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

12y-(+113/y)-7=0

We get rid of parentheses

12y-113/y-7=0

We multiply all the terms by the denominator


12y*y-7*y-113=0

We add all the numbers together, and all the variables

-7y+12y*y-113=0

Wy multiply elements

12y^2-7y-113=0

a = 12; b = -7; c = -113;
Δ = b2-4ac
Δ = -72-4·12·(-113)
Δ = 5473
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{-(-7)-\sqrt{5473}}{2*12}=\frac{7-\sqrt{5473}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{5473}}{2*12}=\frac{7+\sqrt{5473}}{24}
$