12n^2-6n=27

Solution for 12n^2-6n=27 equation:

12n^2-6n=27

We move all terms to the left:

12n^2-6n-(27)=0

a = 12; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·12·(-27)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{37}}{2*12}=\frac{6-6\sqrt{37}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{37}}{2*12}=\frac{6+6\sqrt{37}}{24}
$