12-16/y=y+22

Solution for 12-16/y=y+22 equation:

12-16/y=y+22

We move all terms to the left:

12-16/y-(y+22)=0


Domain of the equation: y!=0

y∈R


We get rid of parentheses

-16/y-y-22+12=0

We multiply all the terms by the denominator


-y*y-22*y+12*y-16=0

We add all the numbers together, and all the variables

-10y-y*y-16=0

Wy multiply elements

-1y^2-10y-16=0

a = -1; b = -10; c = -16;
Δ = b2-4ac
Δ = -102-4·(-1)·(-16)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*-1}=\frac{4}{-2}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*-1}=\frac{16}{-2}
=-8
$