(n^2)+3n=270

Solution for (n^2)+3n=270 equation:

(n^2)+3n=270

We move all terms to the left:

(n^2)+3n-(270)=0

a = 1; b = 3; c = -270;
Δ = b2-4ac
Δ = 32-4·1·(-270)
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{-(3)-33}{2*1}=\frac{-36}{2}
=-18
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+33}{2*1}=\frac{30}{2}
=15
$