-6x2-12x-1=0

Solution for -6x2-12x-1=0 equation:

-6x^2-12x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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