(x-3)(3x+6)=27x+99

Solution for (x-3)(3x+6)=27x+99 equation:

(x-3)(3x+6)=27x+99

We move all terms to the left:

(x-3)(3x+6)-(27x+99)=0

We get rid of parentheses

(x-3)(3x+6)-27x-99=0

We multiply parentheses ..

(+3x^2+6x-9x-18)-27x-99=0

We get rid of parentheses

3x^2+6x-9x-27x-18-99=0

We add all the numbers together, and all the variables

3x^2-30x-117=0

a = 3; b = -30; c = -117;
Δ = b2-4ac
Δ = -302-4·3·(-117)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-48}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+48}{2*3}=\frac{78}{6}
=13
$