10n-n^2=16

Solution for 10n-n^2=16 equation:

10n-n^2=16

We move all terms to the left:

10n-n^2-(16)=0

We add all the numbers together, and all the variables

-1n^2+10n-16=0

a = -1; b = 10; c = -16;
Δ = b2-4ac
Δ = 102-4·(-1)·(-16)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6}{2*-1}=\frac{-16}{-2}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6}{2*-1}=\frac{-4}{-2}
=+2
$