5n^2-81=-12n

Solution for 5n^2-81=-12n equation:

5n^2-81=-12n

We move all terms to the left:

5n^2-81-(-12n)=0

We get rid of parentheses

5n^2+12n-81=0

a = 5; b = 12; c = -81;
Δ = b2-4ac
Δ = 122-4·5·(-81)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-42}{2*5}=\frac{-54}{10}
=-5+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+42}{2*5}=\frac{30}{10}
=3
$