n(2n-4)=30

Solution for n(2n-4)=30 equation:

n(2n-4)=30

We move all terms to the left:

n(2n-4)-(30)=0

We multiply parentheses

2n^2-4n-30=0

a = 2; b = -4; c = -30;
Δ = b2-4ac
Δ = -42-4·2·(-30)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*2}=\frac{-12}{4}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*2}=\frac{20}{4}
=5
$