5n^2-18=27n

Solution for 5n^2-18=27n equation:

5n^2-18=27n

We move all terms to the left:

5n^2-18-(27n)=0

a = 5; b = -27; c = -18;
Δ = b2-4ac
Δ = -272-4·5·(-18)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*5}=\frac{-6}{10}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*5}=\frac{60}{10}
=6
$