6n^2+-54n+120=0

Solution for 6n^2+-54n+120=0 equation:

6n^2+-54n+120=0

We add all the numbers together, and all the variables

6n^2-54n=0

a = 6; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·6·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*6}=\frac{0}{12}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*6}=\frac{108}{12}
=9
$