6n(n-3)-2n=10

Solution for 6n(n-3)-2n=10 equation:

6n(n-3)-2n=10

We move all terms to the left:

6n(n-3)-2n-(10)=0

We add all the numbers together, and all the variables

-2n+6n(n-3)-10=0

We multiply parentheses

6n^2-2n-18n-10=0

We add all the numbers together, and all the variables

6n^2-20n-10=0

a = 6; b = -20; c = -10;
Δ = b2-4ac
Δ = -202-4·6·(-10)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{10}}{2*6}=\frac{20-8\sqrt{10}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{10}}{2*6}=\frac{20+8\sqrt{10}}{12}
$