5n^2-54=-3n

Solution for 5n^2-54=-3n equation:

5n^2-54=-3n

We move all terms to the left:

5n^2-54-(-3n)=0

We get rid of parentheses

5n^2+3n-54=0

a = 5; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·5·(-54)
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{-(3)-33}{2*5}=\frac{-36}{10}
=-3+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+33}{2*5}=\frac{30}{10}
=3
$