-9+12/y=y-13

Solution for -9+12/y=y-13 equation:

-9+12/y=y-13

We move all terms to the left:

-9+12/y-(y-13)=0


Domain of the equation: y!=0

y∈R


We get rid of parentheses

12/y-y+13-9=0

We multiply all the terms by the denominator


-y*y+13*y-9*y+12=0

We add all the numbers together, and all the variables

4y-y*y+12=0

Wy multiply elements

-1y^2+4y+12=0

a = -1; b = 4; c = +12;
Δ = b2-4ac
Δ = 42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-1}=\frac{-12}{-2}
=+6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-1}=\frac{4}{-2}
=-2
$