4(x^2+6x)=-11

Solution for 4(x^2+6x)=-11 equation:

4(x^2+6x)=-11

We move all terms to the left:

4(x^2+6x)-(-11)=0

We add all the numbers together, and all the variables

4(x^2+6x)+11=0

We multiply parentheses

4x^2+24x+11=0

a = 4; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·4·11
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20}{2*4}=\frac{-44}{8}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20}{2*4}=\frac{-4}{8}
=-1/2
$