3n2-6n=6

Solution for 3n2-6n=6 equation:

3n^2-6n=6

We move all terms to the left:

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

a = 3; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·3·(-6)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*3}=\frac{6-6\sqrt{3}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*3}=\frac{6+6\sqrt{3}}{6}
$