n(5n-9)=612

Solution for n(5n-9)=612 equation:

n(5n-9)=612

We move all terms to the left:

n(5n-9)-(612)=0

We multiply parentheses

5n^2-9n-612=0

a = 5; b = -9; c = -612;
Δ = b2-4ac
Δ = -92-4·5·(-612)
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-111}{2*5}=\frac{-102}{10}
=-10+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+111}{2*5}=\frac{120}{10}
=12
$