n(n-3)=304

Solution for n(n-3)=304 equation:

n(n-3)=304

We move all terms to the left:

n(n-3)-(304)=0

We multiply parentheses

n^2-3n-304=0

a = 1; b = -3; c = -304;
Δ = b2-4ac
Δ = -32-4·1·(-304)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-35}{2*1}=\frac{-32}{2}
=-16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+35}{2*1}=\frac{38}{2}
=19
$