n(2n+3)=90

Solution for n(2n+3)=90 equation:

n(2n+3)=90

We move all terms to the left:

n(2n+3)-(90)=0

We multiply parentheses

2n^2+3n-90=0

a = 2; b = 3; c = -90;
Δ = b2-4ac
Δ = 32-4·2·(-90)
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{-(3)-27}{2*2}=\frac{-30}{4}
=-7+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*2}=\frac{24}{4}
=6
$