-3x(x+8)-4=-19

Solution for -3x(x+8)-4=-19 equation:

-3x(x+8)-4=-19

We move all terms to the left:

-3x(x+8)-4-(-19)=0

We add all the numbers together, and all the variables

-3x(x+8)+15=0

We multiply parentheses

-3x^2-24x+15=0

a = -3; b = -24; c = +15;
Δ = b2-4ac
Δ = -242-4·(-3)·15
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{21}}{2*-3}=\frac{24-6\sqrt{21}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{21}}{2*-3}=\frac{24+6\sqrt{21}}{-6}
$