(24-y)y=128

Solution for (24-y)y=128 equation:

(24-y)y=128

We move all terms to the left:

(24-y)y-(128)=0

We add all the numbers together, and all the variables

(-1y+24)y-128=0

We multiply parentheses

-1y^2+24y-128=0

a = -1; b = 24; c = -128;
Δ = b2-4ac
Δ = 242-4·(-1)·(-128)
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{-(24)-8}{2*-1}=\frac{-32}{-2}
=+16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8}{2*-1}=\frac{-16}{-2}
=+8
$