12n^2+36n+12=0

Solution for 12n^2+36n+12=0 equation:

12n^2+36n+12=0

a = 12; b = 36; c = +12;
Δ = b2-4ac
Δ = 362-4·12·12
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{5}}{2*12}=\frac{-36-12\sqrt{5}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{5}}{2*12}=\frac{-36+12\sqrt{5}}{24}
$