6n(n-4)=-20

Solution for 6n(n-4)=-20 equation:

6n(n-4)=-20

We move all terms to the left:

6n(n-4)-(-20)=0

We add all the numbers together, and all the variables

6n(n-4)+20=0

We multiply parentheses

6n^2-24n+20=0

a = 6; b = -24; c = +20;
Δ = b2-4ac
Δ = -242-4·6·20
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{6}}{2*6}=\frac{24-4\sqrt{6}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{6}}{2*6}=\frac{24+4\sqrt{6}}{12}
$