(2x-6)(2x+10)=180

Solution for (2x-6)(2x+10)=180 equation:

(2x-6)(2x+10)=180

We move all terms to the left:

(2x-6)(2x+10)-(180)=0

We multiply parentheses ..

(+4x^2+20x-12x-60)-180=0

We get rid of parentheses

4x^2+20x-12x-60-180=0

We add all the numbers together, and all the variables

4x^2+8x-240=0

a = 4; b = 8; c = -240;
Δ = b2-4ac
Δ = 82-4·4·(-240)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{61}}{2*4}=\frac{-8-8\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{61}}{2*4}=\frac{-8+8\sqrt{61}}{8}
$