n^2-21n-72=0

Solution for n^2-21n-72=0 equation:

n^2-21n-72=0

a = 1; b = -21; c = -72;
Δ = b2-4ac
Δ = -212-4·1·(-72)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-27}{2*1}=\frac{-6}{2}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*1}=\frac{48}{2}
=24
$