(x+4)(-5x-6)=-30

Solution for (x+4)(-5x-6)=-30 equation:

(x+4)(-5x-6)=-30

We move all terms to the left:

(x+4)(-5x-6)-(-30)=0

We add all the numbers together, and all the variables

(x+4)(-5x-6)+30=0

We multiply parentheses ..

(-5x^2-6x-20x-24)+30=0

We get rid of parentheses

-5x^2-6x-20x-24+30=0

We add all the numbers together, and all the variables

-5x^2-26x+6=0

a = -5; b = -26; c = +6;
Δ = b2-4ac
Δ = -262-4·(-5)·6
Δ = 796
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:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{199}}{2*-5}=\frac{26-2\sqrt{199}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{199}}{2*-5}=\frac{26+2\sqrt{199}}{-10}
$