n(n+9)=90

Solution for n(n+9)=90 equation:

n(n+9)=90

We move all terms to the left:

n(n+9)-(90)=0

We multiply parentheses

n^2+9n-90=0

a = 1; b = 9; c = -90;
Δ = b2-4ac
Δ = 92-4·1·(-90)
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{-(9)-21}{2*1}=\frac{-30}{2}
=-15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*1}=\frac{12}{2}
=6
$