Y=16x-1-4x^2

Solution for Y=16x-1-4x^2 equation:

=16Y-1-4Y^2

We move all terms to the left:

-(16Y-1-4Y^2)=0

We get rid of parentheses

4Y^2-16Y+1=0

a = 4; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·4·1
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{15}}{2*4}=\frac{16-4\sqrt{15}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{15}}{2*4}=\frac{16+4\sqrt{15}}{8}
$