(x-3)(x+9)=-24

Solution for (x-3)(x+9)=-24 equation:

(x-3)(x+9)=-24

We move all terms to the left:

(x-3)(x+9)-(-24)=0

We add all the numbers together, and all the variables

(x-3)(x+9)+24=0

We multiply parentheses ..

(+x^2+9x-3x-27)+24=0

We get rid of parentheses

x^2+9x-3x-27+24=0

We add all the numbers together, and all the variables

x^2+6x-3=0

a = 1; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·1·(-3)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*1}=\frac{-6-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*1}=\frac{-6+4\sqrt{3}}{2}
$