(2x-4)(2x+6)=36

Solution for (2x-4)(2x+6)=36 equation:

(2x-4)(2x+6)=36

We move all terms to the left:

(2x-4)(2x+6)-(36)=0

We multiply parentheses ..

(+4x^2+12x-8x-24)-36=0

We get rid of parentheses

4x^2+12x-8x-24-36=0

We add all the numbers together, and all the variables

4x^2+4x-60=0

a = 4; b = 4; c = -60;
Δ = b2-4ac
Δ = 42-4·4·(-60)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{61}}{2*4}=\frac{-4-4\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{61}}{2*4}=\frac{-4+4\sqrt{61}}{8}
$