3n^2=-9n+54

Solution for 3n^2=-9n+54 equation:

3n^2=-9n+54

We move all terms to the left:

3n^2-(-9n+54)=0

We get rid of parentheses

3n^2+9n-54=0

a = 3; b = 9; c = -54;
Δ = b2-4ac
Δ = 92-4·3·(-54)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-27}{2*3}=\frac{-36}{6}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+27}{2*3}=\frac{18}{6}
=3
$