Y=128x^2-2

Solution for Y=128x^2-2 equation:

=128Y^2-2

We move all terms to the left:

-(128Y^2-2)=0

We get rid of parentheses

-128Y^2+2=0

a = -128; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-128)·2
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*-128}=\frac{-32}{-256}
=1/8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*-128}=\frac{32}{-256}
=-1/8
$