(2x+6)(8x-102)=180

Solution for (2x+6)(8x-102)=180 equation:

(2x+6)(8x-102)=180

We move all terms to the left:

(2x+6)(8x-102)-(180)=0

We multiply parentheses ..

(+16x^2-204x+48x-612)-180=0

We get rid of parentheses

16x^2-204x+48x-612-180=0

We add all the numbers together, and all the variables

16x^2-156x-792=0

a = 16; b = -156; c = -792;
Δ = b2-4ac
Δ = -1562-4·16·(-792)
Δ = 75024
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:

$\sqrt{\Delta}=\sqrt{75024}=\sqrt{144*521}=\sqrt{144}*\sqrt{521}=12\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-12\sqrt{521}}{2*16}=\frac{156-12\sqrt{521}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+12\sqrt{521}}{2*16}=\frac{156+12\sqrt{521}}{32}
$