n^2+3n=460

Solution for n^2+3n=460 equation:

n^2+3n=460

We move all terms to the left:

n^2+3n-(460)=0

a = 1; b = 3; c = -460;
Δ = b2-4ac
Δ = 32-4·1·(-460)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-43}{2*1}=\frac{-46}{2}
=-23
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+43}{2*1}=\frac{40}{2}
=20
$