n^2-5n=16

Solution for n^2-5n=16 equation:

n^2-5n=16

We move all terms to the left:

n^2-5n-(16)=0

a = 1; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·1·(-16)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{89}}{2*1}=\frac{5-\sqrt{89}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{89}}{2*1}=\frac{5+\sqrt{89}}{2}
$