6(x+11)x=-6

Solution for 6(x+11)x=-6 equation:

6(x+11)x=-6

We move all terms to the left:

6(x+11)x-(-6)=0

We add all the numbers together, and all the variables

6(x+11)x+6=0

We multiply parentheses

6x^2+66x+6=0

a = 6; b = 66; c = +6;
Δ = b2-4ac
Δ = 662-4·6·6
Δ = 4212
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:

$\sqrt{\Delta}=\sqrt{4212}=\sqrt{324*13}=\sqrt{324}*\sqrt{13}=18\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-18\sqrt{13}}{2*6}=\frac{-66-18\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+18\sqrt{13}}{2*6}=\frac{-66+18\sqrt{13}}{12}
$