n^2-n-272=0

Solution for n^2-n-272=0 equation:

n^2-n-272=0

We add all the numbers together, and all the variables

n^2-1n-272=0

a = 1; b = -1; c = -272;
Δ = b2-4ac
Δ = -12-4·1·(-272)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-33}{2*1}=\frac{-32}{2}
=-16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+33}{2*1}=\frac{34}{2}
=17
$