6n^2=20+6n

Solution for 6n^2=20+6n equation:

6n^2=20+6n

We move all terms to the left:

6n^2-(20+6n)=0

We add all the numbers together, and all the variables

6n^2-(6n+20)=0

We get rid of parentheses

6n^2-6n-20=0

a = 6; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·6·(-20)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{129}}{2*6}=\frac{6-2\sqrt{129}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{129}}{2*6}=\frac{6+2\sqrt{129}}{12}
$