48=y(16-y)

Solution for 48=y(16-y) equation:

48=y(16-y)

We move all terms to the left:

48-(y(16-y))=0

We add all the numbers together, and all the variables

-(y(-1y+16))+48=0


We calculate terms in parentheses: -(y(-1y+16)), so:

y(-1y+16)

We multiply parentheses

-1y^2+16y

Back to the equation:

-(-1y^2+16y)


We get rid of parentheses

1y^2-16y+48=0

We add all the numbers together, and all the variables

y^2-16y+48=0

a = 1; b = -16; c = +48;
Δ = b2-4ac
Δ = -162-4·1·48
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{-(-16)-8}{2*1}=\frac{8}{2}
=4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*1}=\frac{24}{2}
=12
$