n^2+17n+72n=0

Solution for n^2+17n+72n=0 equation:

n^2+17n+72n=0

We add all the numbers together, and all the variables

n^2+89n=0

a = 1; b = 89; c = 0;
Δ = b2-4ac
Δ = 892-4·1·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-89}{2*1}=\frac{-178}{2}
=-89
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+89}{2*1}=\frac{0}{2}
=0
$