(2x+4)(2x-4)=2x+9

Solution for (2x+4)(2x-4)=2x+9 equation:

(2x+4)(2x-4)=2x+9

We move all terms to the left:

(2x+4)(2x-4)-(2x+9)=0

We use the square of the difference formula

4x^2-(2x+9)-16=0

We get rid of parentheses

4x^2-2x-9-16=0

We add all the numbers together, and all the variables

4x^2-2x-25=0

a = 4; b = -2; c = -25;
Δ = b2-4ac
Δ = -22-4·4·(-25)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{101}}{2*4}=\frac{2-2\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{101}}{2*4}=\frac{2+2\sqrt{101}}{8}
$