(x+6)+2x(x+6)=72

Solution for (x+6)+2x(x+6)=72 equation:

(x+6)+2x(x+6)=72

We move all terms to the left:

(x+6)+2x(x+6)-(72)=0

We multiply parentheses

2x^2+(x+6)+12x-72=0

We get rid of parentheses

2x^2+x+12x+6-72=0

We add all the numbers together, and all the variables

2x^2+13x-66=0

a = 2; b = 13; c = -66;
Δ = b2-4ac
Δ = 132-4·2·(-66)
Δ = 697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{697}}{2*2}=\frac{-13-\sqrt{697}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{697}}{2*2}=\frac{-13+\sqrt{697}}{4}
$