n(n-7)=16

Solution for n(n-7)=16 equation:

n(n-7)=16

We move all terms to the left:

n(n-7)-(16)=0

We multiply parentheses

n^2-7n-16=0

a = 1; b = -7; c = -16;
Δ = b2-4ac
Δ = -72-4·1·(-16)
Δ = 113
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{-(-7)-\sqrt{113}}{2*1}=\frac{7-\sqrt{113}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{113}}{2*1}=\frac{7+\sqrt{113}}{2}
$