4n^2-32n+15=-1

Solution for 4n^2-32n+15=-1 equation:

4n^2-32n+15=-1

We move all terms to the left:

4n^2-32n+15-(-1)=0

We add all the numbers together, and all the variables

4n^2-32n+16=0

a = 4; b = -32; c = +16;
Δ = b2-4ac
Δ = -322-4·4·16
Δ = 768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{3}}{2*4}=\frac{32-16\sqrt{3}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{3}}{2*4}=\frac{32+16\sqrt{3}}{8}
$