n2-27n+72=0

Solution for n2-27n+72=0 equation:

n2-27n+72=0

We add all the numbers together, and all the variables

n^2-27n+72=0

a = 1; b = -27; c = +72;
Δ = b2-4ac
Δ = -272-4·1·72
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-21}{2*1}=\frac{6}{2}
=3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*1}=\frac{48}{2}
=24
$