6x(x+4)=(-11)

Solution for 6x(x+4)=(-11) equation:

6x(x+4)=(-11)

We move all terms to the left:

6x(x+4)-((-11))=0

We add all the numbers together, and all the variables

6x(x+4)+11=0

We multiply parentheses

6x^2+24x+11=0

a = 6; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·6·11
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{78}}{2*6}=\frac{-24-2\sqrt{78}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{78}}{2*6}=\frac{-24+2\sqrt{78}}{12}
$