-48/y=8-y

Solution for -48/y=8-y equation:

-48/y=8-y

We move all terms to the left:

-48/y-(8-y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-48/y-(-1y+8)=0

We get rid of parentheses

-48/y+1y-8=0

We multiply all the terms by the denominator


1y*y-8*y-48=0

We add all the numbers together, and all the variables

-8y+1y*y-48=0

Wy multiply elements

y^2-8y-48=0

a = 1; b = -8; c = -48;
Δ = b2-4ac
Δ = -82-4·1·(-48)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*1}=\frac{-8}{2}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*1}=\frac{24}{2}
=12
$