32-2y=126/y

Solution for 32-2y=126/y equation:

32-2y=126/y

We move all terms to the left:

32-2y-(126/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

-2y-(+126/y)+32=0

We get rid of parentheses

-2y-126/y+32=0

We multiply all the terms by the denominator


-2y*y+32*y-126=0

We add all the numbers together, and all the variables

32y-2y*y-126=0

Wy multiply elements

-2y^2+32y-126=0

a = -2; b = 32; c = -126;
Δ = b2-4ac
Δ = 322-4·(-2)·(-126)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4}{2*-2}=\frac{-36}{-4}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4}{2*-2}=\frac{-28}{-4}
=+7
$