6n^2+24n+9=0

Solution for 6n^2+24n+9=0 equation:

6n^2+24n+9=0

a = 6; b = 24; c = +9;
Δ = b2-4ac
Δ = 242-4·6·9
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{10}}{2*6}=\frac{-24-6\sqrt{10}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{10}}{2*6}=\frac{-24+6\sqrt{10}}{12}
$