6n2=-12n-1

Solution for 6n2=-12n-1 equation:

6n^2=-12n-1

We move all terms to the left:

6n^2-(-12n-1)=0

We get rid of parentheses

6n^2+12n+1=0

a = 6; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·6·1
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{30}}{2*6}=\frac{-12-2\sqrt{30}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{30}}{2*6}=\frac{-12+2\sqrt{30}}{12}
$