(3x+6)(2x+18)=24

Solution for (3x+6)(2x+18)=24 equation:

(3x+6)(2x+18)=24

We move all terms to the left:

(3x+6)(2x+18)-(24)=0

We multiply parentheses ..

(+6x^2+54x+12x+108)-24=0

We get rid of parentheses

6x^2+54x+12x+108-24=0

We add all the numbers together, and all the variables

6x^2+66x+84=0

a = 6; b = 66; c = +84;
Δ = b2-4ac
Δ = 662-4·6·84
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{65}}{2*6}=\frac{-66-6\sqrt{65}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{65}}{2*6}=\frac{-66+6\sqrt{65}}{12}
$