(3x+6)(x+4)=36

Solution for (3x+6)(x+4)=36 equation:

(3x+6)(x+4)=36

We move all terms to the left:

(3x+6)(x+4)-(36)=0

We multiply parentheses ..

(+3x^2+12x+6x+24)-36=0

We get rid of parentheses

3x^2+12x+6x+24-36=0

We add all the numbers together, and all the variables

3x^2+18x-12=0

a = 3; b = 18; c = -12;
Δ = b2-4ac
Δ = 182-4·3·(-12)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{13}}{2*3}=\frac{-18-6\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{13}}{2*3}=\frac{-18+6\sqrt{13}}{6}
$