-6x2-12x=-11

Solution for -6x2-12x=-11 equation:

-6x^2-12x=-11

We move all terms to the left:

-6x^2-12x-(-11)=0

We add all the numbers together, and all the variables

-6x^2-12x+11=0

a = -6; b = -12; c = +11;
Δ = b2-4ac
Δ = -122-4·(-6)·11
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{102}}{2*-6}=\frac{12-2\sqrt{102}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{102}}{2*-6}=\frac{12+2\sqrt{102}}{-12}
$