Y=4x^2+16x-1

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

=4Y^2+16Y-1

We move all terms to the left:

-(4Y^2+16Y-1)=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 = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{17}}{2*-4}=\frac{16-4\sqrt{17}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{17}}{2*-4}=\frac{16+4\sqrt{17}}{-8}
$