480=3n^2-90n-720

Solution for 480=3n^2-90n-720 equation:

480=3n^2-90n-720

We move all terms to the left:

480-(3n^2-90n-720)=0

We get rid of parentheses

-3n^2+90n+720+480=0

We add all the numbers together, and all the variables

-3n^2+90n+1200=0

a = -3; b = 90; c = +1200;
Δ = b2-4ac
Δ = 902-4·(-3)·1200
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-150}{2*-3}=\frac{-240}{-6}
=+40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+150}{2*-3}=\frac{60}{-6}
=-10
$