S=-4n^2+16n-12

Solution for S=-4n^2+16n-12 equation:

=-4S^2+16S-12

We move all terms to the left:

-(-4S^2+16S-12)=0

We get rid of parentheses

4S^2-16S+12=0

a = 4; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·4·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*4}=\frac{8}{8}
=1
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*4}=\frac{24}{8}
=3
$