Y=128x+-16x2

Solution for Y=128x+-16x2 equation:

=128Y+-16Y^2

We move all terms to the left:

-(128Y+-16Y^2)=0

We use the square of the difference formula

-(128Y-16Y^2)=0

We get rid of parentheses

16Y^2-128Y=0

a = 16; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·16·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*16}=\frac{256}{32}
=8
$