3n^2=81n

Solution for 3n^2=81n equation:

3n^2=81n

We move all terms to the left:

3n^2-(81n)=0

a = 3; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·3·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*3}=\frac{162}{6}
=27
$