(2x+4)(x+2)=81

Solution for (2x+4)(x+2)=81 equation:

(2x+4)(x+2)=81

We move all terms to the left:

(2x+4)(x+2)-(81)=0

We multiply parentheses ..

(+2x^2+4x+4x+8)-81=0

We get rid of parentheses

2x^2+4x+4x+8-81=0

We add all the numbers together, and all the variables

2x^2+8x-73=0

a = 2; b = 8; c = -73;
Δ = b2-4ac
Δ = 82-4·2·(-73)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-18\sqrt{2}}{2*2}=\frac{-8-18\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+18\sqrt{2}}{2*2}=\frac{-8+18\sqrt{2}}{4}
$