0=-6n^2+78n-216

Solution for 0=-6n^2+78n-216 equation:

0=-6n^2+78n-216

We move all terms to the left:

0-(-6n^2+78n-216)=0

We add all the numbers together, and all the variables

-(-6n^2+78n-216)=0

We get rid of parentheses

6n^2-78n+216=0

a = 6; b = -78; c = +216;
Δ = b2-4ac
Δ = -782-4·6·216
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-30}{2*6}=\frac{48}{12}
=4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+30}{2*6}=\frac{108}{12}
=9
$